Number Series Questions in English

(C) The pattern followed in the series is as follows:
$14 \times 1 - 2 = 12$
$12 \times 2 - 3 = 21$
$21 \times 3 - 4 = 59$
$59 \times 4 - 5 = 231$
$231 \times 5 - 6 = 1149$
Following this logic,the next term is:
$1149 \times 6 - 7 = 6894 - 7 = 6887$

(B) The given series consists of cubes of even numbers starting from $12$.
$12^3 = 12 \times 12 \times 12 = 1728$
$14^3 = 14 \times 14 \times 14 = 2744$
$16^3 = 16 \times 16 \times 16 = 4096$
$18^3 = 18 \times 18 \times 18 = 5832$
$20^3 = 20 \times 20 \times 20 = 8000$
$22^3 = 22 \times 22 \times 22 = 10648$
Following this pattern,the next term is $24^3$.
$24^3 = 24 \times 24 \times 24 = 13824$.

(C) The pattern in the series is as follows:
$120 \div 8 = 15$
$15 \times 7 = 105$
$105 \div 6 = 17.5$
$17.5 \times 5 = 87.5$
Following the alternating pattern of division and multiplication with decreasing integers $(8, 7, 6, 5, 4)$:
The next operation is division by $4$.
$87.5 \div 4 = 21.875$

(D) The series follows a pattern of pairs where the difference increases by $4$ in each subsequent pair.
Pair $1$: $3, 6$ (Difference = $3$)
Pair $2$: $21, 28$ (Difference = $7$)
Pair $3$: $55, 66$ (Difference = $11$)
Pair $4$: $x, 120$ (Difference = $15$)
Since the differences are $3, 7, 11, 15$ (an arithmetic progression with a common difference of $4$),the next difference must be $15$.
Therefore,$x = 120 - 15 = 105$.

(D) The given sequence is: $529, 841, 961, 1369, 1681, 1849, \dots$
These numbers are squares of consecutive prime numbers starting from $23$:
$23^2 = 529$
$29^2 = 841$
$31^2 = 961$
$37^2 = 1369$
$41^2 = 1681$
$43^2 = 1849$
The next prime number after $43$ is $47$.
Therefore,the next term is $47^2 = 2209$.

(C) The pattern follows the rule: $(n_i \times x + y \times x)$,where $x$ decreases by $1$ starting from $7$,and $y$ increases by $1$ starting from $2$.
Step $1$: $3 \times 7 + 2 \times 7 = 21 + 14 = 35$
Step $2$: $35 \times 6 + 3 \times 6 = 210 + 18 = 228$ (Instead of $226$)
Step $3$: $228 \times 5 + 4 \times 5 = 1140 + 20 = 1160$
Step $4$: $1160 \times 4 + 5 \times 4 = 4640 + 20 = 4660$
Step $5$: $4660 \times 3 + 6 \times 3 = 13980 + 18 = 13998$
Thus,the wrong number in the series is $226$.

(B) The pattern follows the rule: $n_{i} \times (8-i) - (8-i)$,where $i$ is the step index starting from $1$.
Step $1$: $18 \times 7 - 7 = 126 - 7 = 119$
Step $2$: $119 \times 6 - 6 = 714 - 6 = 708$
Step $3$: $708 \times 5 - 5 = 3540 - 5 = 3535$
Step $4$: $3535 \times 4 - 4 = 14140 - 4 = 14136$
Step $5$: $14136 \times 3 - 3 = 42408 - 3 = 42405$
Comparing the calculated values with the given series,$3534$ is incorrect as it should be $3535$.

(C) The pattern followed in the series is: $(n \times \text{position}) + (\text{position} + 1)$.
$4 \times 1 + 2 = 6$
$6 \times 2 + 3 = 15$ (which is not $18$)
$15 \times 3 + 4 = 49$
$49 \times 4 + 5 = 201$
$201 \times 5 + 6 = 1011$
Since $15$ should be in the place of $18$, the wrong number is $18$.

(A) The pattern follows the logic: $(x_n \times k) + (y_n \times k)$,where $k$ decreases by $1$ at each step.
$2 \times 6 + 7 \times 6 = 12 + 42 = 54$
$54 \times 5 + 6 \times 5 = 270 + 30 = 300$
$300 \times 4 + 5 \times 4 = 1200 + 20 = 1220$
$1220 \times 3 + 4 \times 3 = 3660 + 12 = 3672$
Since $3672 \neq 3674$,the number $3674$ is incorrect.
Checking the next term: $3672 \times 2 + 3 \times 2 = 7344 + 6 = 7350$,which matches the series.

(D) Let the given series be $0, 5, 18, 43, 84, 145, ?$.
Calculate the differences between consecutive terms:
$5 - 0 = 5$
$18 - 5 = 13$
$43 - 18 = 25$
$84 - 43 = 41$
$145 - 84 = 61$
The differences are $5, 13, 25, 41, 61$.
Now,find the second-order differences:
$13 - 5 = 8$
$25 - 13 = 12$
$41 - 25 = 16$
$61 - 41 = 20$
The second-order differences are $8, 12, 16, 20$,which form an arithmetic progression with a common difference of $4$.
The next second-order difference will be $20 + 4 = 24$.
Therefore,the next first-order difference will be $61 + 24 = 85$.
The next term in the series is $145 + 85 = 230$.

(D) The pattern followed in the series is:
$10 \times 1 + (1 \times 7) = 10 + 7 = 17$
$17 \times 2 + (2 \times 7) = 34 + 14 = 48$
$48 \times 3 + (3 \times 7) = 144 + 21 = 165$
$165 \times 4 + (4 \times 7) = 660 + 28 = 688$
$688 \times 5 + (5 \times 7) = 3440 + 35 = 3475$
Following this pattern,the next term is:
$3475 \times 6 + (6 \times 7) = 20850 + 42 = 20892$

(C) The pattern is based on multiplying by consecutive multiples of $3$ with an increasing gap.
$1 \times 3 = 3$
$3 \times 8 = 24$
$24 \times 15 = 360$
$360 \times 24 = 8640$
$8640 \times 35 = 302400$
Let us analyze the multipliers: $3, 8, 15, 24, 35, ...$
The differences between these multipliers are: $8-3=5$,$15-8=7$,$24-15=9$,$35-24=11$.
The next difference should be $13$.
So,the next multiplier is $35 + 13 = 48$.
Therefore,the next term is $302400 \times 48 = 14515200$.

(B) The pattern follows the rule: $(\text{Term} \times n) + (2 \times n)$,where $n$ is the position index starting from $1$.
$12 \times 1 + 2 \times 1 = 12 + 2 = 14$
$14 \times 2 + 2 \times 2 = 28 + 4 = 32$
$32 \times 3 + 2 \times 3 = 96 + 6 = 102$
$102 \times 4 + 2 \times 4 = 408 + 8 = 416$
$416 \times 5 + 2 \times 5 = 2080 + 10 = 2090$
Following this pattern,the next term is:
$2090 \times 6 + 2 \times 6 = 12540 + 12 = 12552$

(A) The pattern of the series is as follows:
$10 \times \frac{3}{2} = 15$
$15 \times \frac{4}{4} = 15$
$15 \times \frac{5}{6} = 12.5$
$12.5 \times \frac{6}{8} = 9.375$
$9.375 \times \frac{7}{10} = 6.5625$
Following this pattern,the next term is multiplied by $\frac{8}{12}$:
$6.5625 \times \frac{8}{12} = 6.5625 \times \frac{2}{3} = 4.375$

(D) The pattern of the series is as follows:
$3 \times 7 + 1 = 22$
$22 \times 6 + 2 = 134$
$134 \times 5 + 3 = 673$
$673 \times 4 + 4 = 2696$
$2696 \times 3 + 5 = 8093$
Thus,the missing term is $134$.

(A) The pattern follows the rule: $(\text{Previous Term} \times n) + (n \times (8-n))$,where $n$ is the position index starting from $1$.
For $n=1$: $(6 \times 1) + (1 \times 7) = 6 + 7 = 13$.
For $n=2$: $(13 \times 2) + (2 \times 6) = 26 + 12 = 38$.
For $n=3$: $(38 \times 3) + (3 \times 5) = 114 + 15 = 129$.
For $n=4$: $(129 \times 4) + (4 \times 4) = 516 + 16 = 532$.
For $n=5$: $(532 \times 5) + (5 \times 3) = 2660 + 15 = 2675$.
Thus,the missing number is $129$.

(C) The pattern followed in the series is:
$17 \times 0.5 + 0.5 = 9$
$9 \times 1 + 1 = 10$
$10 \times 1.5 + 1.5 = 16.5$
$16.5 \times 2 + 2 = 35$
$35 \times 2.5 + 2.5 = 90$
Following this logic,the missing term is $10$.

(A) The pattern of the series is as follows:
$3 \times 1 + 1^2 = 3 + 1 = 4$
$4 \times 2 + 2^2 = 8 + 4 = 12$
$12 \times 3 + 3^2 = 36 + 9 = 45$
$45 \times 4 + 4^2 = 180 + 16 = 196$
Following this logic,the missing term is $45$.

(B) The pattern in the given number series is as follows:
$16 \times 0.5 = 8$
$8 \times 1.5 = 12$
$12 \times 2.5 = 30$
Following this pattern,the next term is calculated by multiplying by $3.5$:
$30 \times 3.5 = 105$
Therefore,the missing number is $105$.

(A) The pattern follows the logic: $n_{i} \times i + i \times (6-i)$,where $i$ is the position index starting from $1$.
For the first term: $7 \times 1 + 1 \times 5 = 7 + 5 = 12$.
For the second term: $12 \times 2 + 2 \times 4 = 24 + 8 = 32$.
For the third term: $32 \times 3 + 3 \times 3 = 96 + 9 = 105$.
For the fourth term: $105 \times 4 + 4 \times 2 = 420 + 8 = 428$.
Thus,the next term is $428$.

(A) The given sequence consists of the squares of consecutive prime numbers.
The sequence is: $2^{2}, 3^{2}, 5^{2}, ?, 11^{2}, 13^{2}, 17^{2}, 19^{2}$.
The prime numbers in order are $2, 3, 5, 7, 11, 13, 17, 19$.
The missing term corresponds to the square of the prime number $7$.
Therefore,the missing term is $7^{2} = 49$.

(A) The pattern of the series is based on the sum of the two preceding terms plus an incrementing constant.
Let the terms be $T_1, T_2, T_3, T_4, T_5, T_6$.
$T_3 = T_1 + T_2 + 2 = 3 + 8 + 2 = 13$
$T_4 = T_2 + T_3 + 3 = 8 + 13 + 3 = 24$
$T_5 = T_3 + T_4 + 4 = 13 + 24 + 4 = 41$
$T_6 = T_4 + T_5 + 5 = 24 + 41 + 5 = 70$
Thus,the missing term is $70$.

(C) The given sequence is a combination of two alternating series:
First series: $45, 47, 49, 51, 53$ (each term increases by $2$).
Second series: $54, ?, 56, 57$ (this is a sequence of consecutive integers).
In the second series,the terms are $54, 55, 56, 57$.
Therefore,the missing term is $55$.

(A) The series follows a pattern where the terms at even positions are the product of their adjacent terms.
$6 \times 3 = 18$
$3 \times 7 = 21$
$7 \times ? = 56$
To find the missing term,we solve for $?$: $? = 56 / 7 = 8$.
Therefore,the next term is $8$.

(B) The given sequence is a combination of two alternating series:
$1^{st}$ series: $2, 4, 6, \dots$ (Even numbers increasing by $2$)
The next term in this series is $6 + 2 = 8$.
$2^{nd}$ series: $15, 12, 7, \dots$
The pattern of differences is: $15 - 3 = 12$,$12 - 5 = 7$.
The next difference should be $-7$.
So,the next term is $7 - 7 = 0$.
Therefore,the missing terms are $8$ and $0$.

(A) The given sequence is a combination of two alternating series.
Series $1$: $20, 19, 17, 14, ?$
Pattern: $20 \xrightarrow{-1} 19 \xrightarrow{-2} 17 \xrightarrow{-3} 14 \xrightarrow{-4} 10$
So,the first missing term is $10$.
Series $2$: $20, 16, 13, 11, ?$
Pattern: $20 \xrightarrow{-4} 16 \xrightarrow{-3} 13 \xrightarrow{-2} 11 \xrightarrow{-1} 10$
So,the second missing term is $10$.
Therefore,the missing numbers are $10, 10$.

(D) The given series is a combination of two alternating series:
$(i)$ The first series consists of the terms at odd positions: $0, 3, 8, 15, 24, ?$
The pattern is:
$0 + 3 = 3$
$3 + 5 = 8$
$8 + 7 = 15$
$15 + 9 = 24$
Following this pattern of adding consecutive odd numbers $(3, 5, 7, 9, 11)$,the next term is $24 + 11 = 35$.
$(ii)$ The second series consists of the terms at even positions: $2, 5, 10, 17, 26$
This follows the pattern $(n^2 + 1)$ for $n = 1, 2, 3, 4, 5$ $(1^2+1=2, 2^2+1=5, 3^2+1=10, 4^2+1=17, 5^2+1=26)$.
Since the question asks for the term following $26$,which is the $11^{th}$ term,it belongs to the first series. Thus,the answer is $35$.

(C) The sequence is formed by two different series of consecutive odd numbers placed side-by-side.
The first digits of each term are: $1, 3, 5, 7, 9, 11$.
The second digits of each term are: $3, 5, 7, 9, 11, 13$.
Combining these,the next term in the series is $1113$.

(C) The given series is a combination of two alternating series:
$(i)$ The first series consists of terms at odd positions: $625, 125, 25, 5$. Each term is obtained by dividing the previous term by $5$ $(625 \div 5 = 125, 125 \div 5 = 25, 25 \div 5 = 5)$.
$(ii)$ The second series consists of terms at even positions: $5, 25, ?$. Each term is obtained by multiplying the previous term by $5$ $(5 \times 5 = 25, 25 \times 5 = 125)$.
Therefore,the missing term is $125$.

(B) The given sequence is a combination of two alternating series:
Series $(i)$ consists of the $1^{st}, 3^{rd}, 5^{th}, 7^{th}, 9^{th}$ terms: $3, 7, 13, 21, 31, ...$
Pattern for Series $(i)$: $3 (+4) = 7, 7 (+6) = 13, 13 (+8) = 21, 21 (+10) = 31$.
The next term in this series would be $31 (+12) = 43$.
Series $(ii)$ consists of the $2^{nd}, 4^{th}, 6^{th}, 8^{th}, 10^{th}$ terms: $4, 7, 13, 22, 34, ...$
Pattern for Series $(ii)$: $4 (+3) = 7, 7 (+6) = 13, 13 (+9) = 22, 22 (+12) = 34$.
Since the question mark represents the $11^{th}$ term,it follows the pattern of Series $(i)$.
Therefore,the missing number is $31 + 12 = 43$.

(A) The given series is $11, 10, ?, 100, 1001, 1000, 10001$.
Observe the pattern between consecutive terms:
$11 - 1 = 10$
$10 \times 10 + 1 = 101$
$101 - 1 = 100$
$100 \times 10 + 1 = 1001$
$1001 - 1 = 1000$
$1000 \times 10 + 1 = 10001$
The pattern alternates between subtracting $1$ and multiplying by $10$ then adding $1$.
Therefore,the missing term is $10 \times 10 + 1 = 101$.

(C) The given series is $13, 32, 24, 43, 35, ?, 46, 65, 57, 76$.
This series is a combination of two alternating series:
$(i)$ The first series consists of terms at odd positions: $13, 24, 35, 46, 57$. Here,each term increases by $11$ $(13+11=24, 24+11=35, 35+11=46, 46+11=57)$.
$(ii)$ The second series consists of terms at even positions: $32, 43, ?, 65, 76$. Here,each term also increases by $11$ $(32+11=43, 43+11=54, 54+11=65, 65+11=76)$.
Therefore,the missing term is $43 + 11 = 54$.

(B) The given sequence is a combination of $3$ interleaved series:
$(i)$ $2, 4, 6, 8, ?$
$(ii)$ $1, 4, 7, 10$
$(iii)$ $2, 5, 8, 11$
Analyzing series $(i)$,we see it consists of consecutive even numbers: $2, 4, 6, 8, ...$
The next term in this series follows $8$,which is $10$.
Therefore,the missing term is $10$.

(C) Analyze the pattern of the numerators: $2, 4, ?, 11, 16$. The differences are $4-2=2$,$?-4=x$,$11-?=y$,$16-11=5$. The differences are $2, 3, 4, 5$. Thus,the missing numerator is $4+3=7$.
Analyze the pattern of the denominators: $3, 7, ?, 21, 31$. The differences are $7-3=4$,$?-7=x$,$21-?=y$,$31-21=10$. The differences are $4, 6, 8, 10$. Thus,the missing denominator is $7+6=13$.
Therefore,the missing term is $\frac{7}{13}$.

(C) The given series is $960, 924, 852, 744, 600, 420, ?$.
Let's find the difference between consecutive terms:
$960 - 924 = 36 = 36 \times 1$
$924 - 852 = 72 = 36 \times 2$
$852 - 744 = 108 = 36 \times 3$
$744 - 600 = 144 = 36 \times 4$
$600 - 420 = 180 = 36 \times 5$
The pattern of differences is $36 \times 1, 36 \times 2, 36 \times 3, 36 \times 4, 36 \times 5$.
Following this pattern,the next difference should be $36 \times 6 = 216$.
Therefore,the next term is $420 - 216 = 204$.

(C) To find the missing number,observe the pattern between consecutive terms:
$540 / 1800 = 0.3$
$162 / 540 = 0.3$
$48.6 / 162 = 0.3$
Each term is obtained by multiplying the previous term by $0.3$.
Therefore,the missing number $= 48.6 \times 0.3 = 14.58$.

(C) The given series is $280, 284, 300, ?, 400, 500$.
Let us analyze the differences between consecutive terms:
$284 - 280 = 4 = 2^2$
$300 - 284 = 16 = 4^2$
Following this pattern,the next difference should be $6^2 = 36$.
So,the missing term is $300 + 36 = 336$.
To verify,the next difference should be $8^2 = 64$,but here the difference is $400 - 336 = 64$,which matches $8^2$.
The next difference is $500 - 400 = 100 = 10^2$.
Thus,the pattern is adding consecutive even squares: $+2^2, +4^2, +6^2, +8^2, +10^2$.
The missing term is $336$.

(C) The pattern followed in the series is:
$4 \times 1 + 1^2 = 5$
$5 \times 2 + 2^2 = 14$
$14 \times 3 + 3^2 = 51$
Following this logic,the next term is:
$51 \times 4 + 4^2 = 204 + 16 = 220$
To verify,the next term should be:
$220 \times 5 + 5^2 = 1100 + 25 = 1125$
Thus,the missing term is $220$.

(A) The pattern follows the rule: $\times 6-1, \times 5-1, \times 4-1, \times 3-1, \times 2-1$.
Step $1$: $8 \times 6 - 1 = 48 - 1 = 47$
Step $2$: $47 \times 5 - 1 = 235 - 1 = 234$
Step $3$: $234 \times 4 - 1 = 936 - 1 = 935$
Step $4$: $935 \times 3 - 1 = 2805 - 1 = 2804$
Step $5$: $2804 \times 2 - 1 = 5608 - 1 = 5607$
Thus,the missing term is $2804$.

(C) The pattern of the series is based on the addition of consecutive multiples of $3$ starting from $3$,where each subsequent difference is double the previous one:
$9 - 6 = 3$
$15 - 9 = 6$
$27 - 15 = 12$
$51 - 27 = 24$
Following this pattern,the next difference should be $24 \times 2 = 48$.
Therefore,the next number is $51 + 48 = 99$.

(D) The pattern followed in the series is:
$7 \times 1 + 1 = 8$
$8 \times 2 + 2 = 18$
$18 \times 3 + 3 = 57$
$57 \times 4 + 4 = 232$
$232 \times 5 + 5 = 1165$
Therefore,the missing term is $57$.

(D) To find the pattern, calculate the difference between consecutive terms:
$18 - 11 = 7$
$29 - 18 = 11$
$42 - 29 = 13$
$59 - 42 = 17$
$80 - 59 = 21$
$101 - 80 = 21$
The differences are $7, 11, 13, 17, \dots$ which are consecutive prime numbers.
Following this pattern, the next difference should be $19$ instead of $21$.
$59 + 19 = 78$
Then, the next difference should be $23$.
$78 + 23 = 101$
Since $80$ does not fit the pattern, it is the wrong number.

(B) Let us analyze the pattern of the series:
$2 \times 1 + 7 = 9$
$9 \times 2 + 6 = 24$ (Instead of $32$)
$24 \times 3 + 5 = 77$ (This does not match the next term)
Let us try another pattern:
$(2 + 1) \times 3 = 9$
$(9 + 2) \times 3 = 33$ (Not $32$)
Let us try the pattern: $(Previous \text{ } number \times n) + n^2$:
$2 \times 1 + 1^2 = 3$ (No)
Let us try the pattern: $(Previous \text{ } number \times n) + (n+1)$:
$2 \times 1 + 7 = 9$
$9 \times 2 + 14 = 32$
$32 \times 3 + 9 = 105$
$105 \times 4 + 16 = 436$
$436 \times 5 + 25 = 2205$ (Instead of $2195$)
Wait,let us re-examine the pattern:
$2 \times 1 + 7 = 9$
$9 \times 2 + 14 = 32$
$32 \times 3 + 9 = 105$
$105 \times 4 + 16 = 436$
$436 \times 5 + 25 = 2205$
Actually,the pattern is: $(Previous \text{ } number \times n) + n^2$ is not working. Let us check the differences:
$9-2 = 7$
$32-9 = 23$
$105-32 = 73$
$436-105 = 331$
Correct pattern: $(Previous \text{ } number \times 1) + 7 = 9$
$(9 \times 2) + 14 = 32$
$(32 \times 3) + 21 = 117$ (So $105$ is wrong)
Let us check the provided solution logic again:
$(2+1) \times 3 = 9$
$(9+2) \times 3 = 33$
$(33+3) \times 3 = 108$
Given the options,$32$ is the intended wrong number as it breaks the sequence $2, 9, 33, 108, 437, 2196$.

(D) The pattern of the series is based on multiplication by consecutive odd numbers: $\times 11, \times 9, \times 7, \times 5, \times 3, \times 1$.
Let's verify the terms:
$5 \times 11 = 55$
$55 \times 9 = 495$
$495 \times 7 = 3465$
$3465 \times 5 = 17325$
$17325 \times 3 = 51975$
Comparing this with the given series: $5, 55, 495, 3465, 17325, 34650, 51975$.
We see that $34650$ is the wrong number because the term after $17325$ should be $51975$.

(A) Observe the pattern of the series starting from the third term: $18 \times 3 = 54$,$54 \times 3 = 162$,$162 \times 3 = 486$,and $486 \times 3 = 1458$.
This indicates that each term is obtained by multiplying the previous term by $3$.
If we apply this rule to the first term $(2)$,the second term should be $2 \times 3 = 6$.
Since the given second term is $10$,it is the wrong number in the series.

(C) Let us analyze the differences between consecutive terms in the series:
$12 - 8 = 4$
$24 - 12 = 12$
$46 - 24 = 22$
$72 - 46 = 26$
$108 - 72 = 36$
$152 - 108 = 44$
The pattern of differences is $4, 12, 22, 26, 36, 44$. This does not seem consistent.
Let us look at the differences of the differences:
$12 - 4 = 8$
$22 - 12 = 10$
$26 - 22 = 4$
$36 - 26 = 10$
$44 - 36 = 8$
If we observe the pattern of adding multiples of $4$ (or a constant second difference of $8$),the sequence of differences should be $4, 12, 20, 28, 36, 44$.
Checking the terms with this pattern:
$8 + 4 = 12$
$12 + 12 = 24$
$24 + 20 = 44$ (instead of $46$)
$44 + 28 = 72$
$72 + 36 = 108$
$108 + 44 = 152$
Thus,the wrong number is $46$,which should be $44$.

(D) The given series is $16, 22, 40, 78, 144, ?$.
Let us find the differences between consecutive terms:
$22 - 16 = 6$
$40 - 22 = 18$
$78 - 40 = 38$
$144 - 78 = 66$
Now,let us find the differences of these differences (second-order differences):
$18 - 6 = 12$
$38 - 18 = 20$
$66 - 38 = 28$
The differences of the second-order differences are increasing by $8$ ($20 - 12 = 8$,$28 - 20 = 8$).
Following this pattern,the next difference in the second-order sequence should be $28 + 8 = 36$.
Adding this to the last first-order difference: $66 + 36 = 102$.
Finally,adding this to the last term of the series: $144 + 102 = 246$.
Therefore,the next term is $246$.

(C) The given series is $2, 6, 14, 30, ?, 126, 254$.
Observe the differences between consecutive terms:
$6 - 2 = 4$
$14 - 6 = 8$
$30 - 14 = 16$
The differences are in the form of powers of $2$,i.e.,$2^2, 2^3, 2^4, \dots$
Following this pattern,the next difference should be $2^5 = 32$.
So,the missing number is $30 + 32 = 62$.
To verify,the next difference should be $2^6 = 64$,and $62 + 64 = 126$,which matches the series.
Thus,the missing number is $62$.

(C) The given series is $10, 14, 25, 55, 140, ?$.
Let's find the differences between consecutive terms:
$14 - 10 = 4$
$25 - 14 = 11$
$55 - 25 = 30$
$140 - 55 = 85$
Now,analyze the pattern of these differences: $4, 11, 30, 85, ...$
$4 \times 3 - 1 = 11$
$11 \times 3 - 3 = 30$
$30 \times 3 - 5 = 85$
$85 \times 3 - 7 = 248$
The next difference should be $248$.
Therefore,the next term is $140 + 248 = 388$.

(D) The pattern of the series is as follows:
$2 \times 3 + 5 = 11$
$11 \times 4 - 6 = 38$
$38 \times 5 + 7 = 197$
$197 \times 6 - 8 = 1182 - 8 = 1174$
Since the given number is $1172$ instead of $1174$,$1172$ is the wrong number.
Checking the next term: $1174 \times 7 + 9 = 8218 + 9 = 8227$.
Checking the final term: $8227 \times 8 - 10 = 65816 - 10 = 65806$.
Thus,$1172$ is indeed the incorrect number.