Number Series Questions in English

(D) The given series is $2, 3, 5, 7, ?$.
These numbers are consecutive prime numbers.
$A$ prime number is a natural number greater than $1$ that has no positive divisors other than $1$ and itself.
The prime numbers in order are $2, 3, 5, 7, 11, 13, \dots$.
Therefore,the next prime number after $7$ is $11$.

(D) The given series is $1, 3, 6, 10, 15, ?$.
Observe the differences between consecutive terms:
$3 - 1 = 2$
$6 - 3 = 3$
$10 - 6 = 4$
$15 - 10 = 5$
The differences are increasing by $1$ each time $(2, 3, 4, 5, ...)$.
Following this pattern,the next difference should be $6$.
Therefore,the next term is $15 + 6 = 21$.

(C) The given series is $4, 9, 16, 25, ?$.
These numbers can be written as squares of consecutive integers:
$2^{2} = 4$
$3^{2} = 9$
$4^{2} = 16$
$5^{2} = 25$
The next number in the series should be the square of the next integer,which is $6$.
Therefore,$6^{2} = 36$.
Thus,the missing number is $36$.

(D) The given series is $7, 11, 13, 17, 19, 23, ?$.
Observing the numbers,we can see that these are consecutive prime numbers.
$A$ prime number is a natural number greater than $1$ that has no positive divisors other than $1$ and itself.
The sequence of prime numbers starting from $7$ is $7, 11, 13, 17, 19, 23, 29, \dots$.
Therefore,the next prime number after $23$ is $29$.

(A) The given series is $41, 43, 47, 53, 59, ?$.
Observing the series,we can see that these are consecutive prime numbers.
$41$ is a prime number.
$43$ is the next prime number.
$47$ is the next prime number.
$53$ is the next prime number.
$59$ is the next prime number.
The prime number immediately following $59$ is $61$.
Therefore,the missing number is $61$.

(C) The given series is $3, 6, 11, 18, 27, ?$.
Let us find the difference between consecutive terms:
$6 - 3 = 3$
$11 - 6 = 5$
$18 - 11 = 7$
$27 - 18 = 9$
We observe that the differences are consecutive odd numbers: $3, 5, 7, 9, \dots$
The next difference should be $11$.
Therefore,the next term is $27 + 11 = 38$.

(D) Analyze the difference between consecutive terms:
$9 - 4 = 5$
$19 - 9 = 10$
$34 - 19 = 15$
$54 - 34 = 20$
The differences are in an arithmetic progression with a common difference of $5$: $5, 10, 15, 20, ...$
The next difference should be $20 + 5 = 25$.
Therefore,the next number in the series is $54 + 25 = 79$.

(D) The pattern in the given number series is as follows:
$3 - 2 = +1$
$5 - 3 = +2$
$8 - 5 = +3$
$12 - 8 = +4$
Following this pattern,the next increment should be $+5$.
Therefore,the next number is $12 + 5 = 17$.

(D) The given series is $100, 81, 64, 49, ?$.
These numbers are squares of consecutive integers in descending order:
$10^{2} = 100$
$9^{2} = 81$
$8^{2} = 64$
$7^{2} = 49$
Following this pattern,the next number should be $6^{2} = 36$.
Therefore,the correct option is $D$.

(C) The given series is: $8, 27, 64, 125, 216, 343, ?$
These numbers are cubes of consecutive natural numbers starting from $2$:
$2^3 = 8$
$3^3 = 27$
$4^3 = 64$
$5^3 = 125$
$6^3 = 216$
$7^3 = 343$
Following this pattern,the next number should be $8^3$.
$8^3 = 8 \times 8 \times 8 = 512$.
Therefore,the correct option is $C$.

(A) The given series is $56, 63, 70, 77, ?$.
Observe the difference between consecutive terms:
$63 - 56 = 7$
$70 - 63 = 7$
$77 - 70 = 7$
Since the common difference is $7$,the series follows an arithmetic progression with a common difference of $+7$.
Therefore,the next term is $77 + 7 = 84$.

(C) The given number series is $36, 48, 60, 72, ?$.
First,calculate the difference between consecutive terms:
$48 - 36 = 12$
$60 - 48 = 12$
$72 - 60 = 12$
Since the difference between consecutive terms is constant $(+12)$,this is an arithmetic progression.
To find the next term,add $12$ to the last term:
$72 + 12 = 84$.
Therefore,the missing number is $84$.

(D) Observe the pattern in the given series:
$72 - 54 = 18$
$90 - 72 = 18$
$108 - 90 = 18$
Since the difference between consecutive terms is constant $(18)$,this is an arithmetic progression.
To find the next term,add $18$ to the last term:
$108 + 18 = 126$
Therefore,the correct answer is $126$.

(A) The given series is $2, 4, 8, 16, 32, ...$
This series follows the pattern of powers of $2$:
$2^1 = 2$
$2^2 = 4$
$2^3 = 8$
$2^4 = 16$
$2^5 = 32$
Following this pattern,the next term is $2^6 = 64$.

(D) The given number series is $3, 6, 12, 24, 48, ?$.
Observe the pattern: each term is obtained by multiplying the previous term by $2$.
$3 \times 2 = 6$
$6 \times 2 = 12$
$12 \times 2 = 24$
$24 \times 2 = 48$
Following this pattern,the next number is $48 \times 2 = 96$.

(D) The given series is $10, 14, 18, 22, ?$.
Observe the difference between consecutive terms:
$14 - 10 = 4$
$18 - 14 = 4$
$22 - 18 = 4$
Since the difference is constant $(4)$,this is an arithmetic progression with a common difference of $4$.
To find the next term,add $4$ to the last term:
$22 + 4 = 26$.
Therefore,the missing number is $26$.

(C) The given series is $100, 99, 97, 94, 90, ?$.
Observe the pattern of differences between consecutive terms:
$100 - 99 = 1$
$99 - 97 = 2$
$97 - 94 = 3$
$94 - 90 = 4$
The differences are decreasing by $1$ each time,following the sequence $-1, -2, -3, -4, \dots$.
Therefore,the next difference should be $-5$.
Calculating the next term: $90 - 5 = 85$.

(A) The given series is $3, 9, 27, 81, ?$.
Observing the pattern,each term is a power of $3$:
$3^1 = 3$
$3^2 = 9$
$3^3 = 27$
$3^4 = 81$
Following this pattern,the next term should be $3^5$.
$3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243$.
Therefore,the missing number is $243$.

(C) The given number series is $24, 48, 72, 96, ?$.
Observing the pattern,we can see that each term is a multiple of $24$:
$24 \times 1 = 24$
$24 \times 2 = 48$
$24 \times 3 = 72$
$24 \times 4 = 96$
Following this pattern,the next term will be $24 \times 5 = 120$.
Therefore,the correct option is $C$.

(D) The pattern in the given series is as follows:
$78 + 10 = 88$
$88 + 11 = 99$
$99 + 12 = 111$
Following this pattern,the next term should be:
$111 + 13 = 124$
Therefore,the missing number is $124$.

(C) The given series is a geometric progression where each term is obtained by dividing the previous term by $2$.
$512 \div 2 = 256$
$256 \div 2 = 128$
$128 \div 2 = 64$
$64 \div 2 = 32$
Following the same pattern,the next term is $32 \div 2 = 16$.

(C) The given series is $1, 12, 123, 1234, \dots$
Observing the pattern,each term is formed by appending the next natural number to the end of the previous term.
- The first term is $1$.
- The second term is $1$ followed by $2$,which is $12$.
- The third term is $12$ followed by $3$,which is $123$.
- The fourth term is $123$ followed by $4$,which is $1234$.
Following this logic,the next term is $1234$ followed by $5$,which is $12345$.

(A) The pattern involves removing digits alternatively from the left and right ends of the number.
$1$. Starting with $123456$,remove the first digit $(1)$ to get $23456$.
$2$. From $23456$,remove the last digit $(6)$ to get $2345$.
$3$. From $2345$,remove the first digit $(2)$ to get $345$.
$4$. Following the pattern,from $345$,remove the last digit $(5)$ to get $34$.
Therefore,the next number is $34$.

(A) The given series is $35, 49, 63, 77, \dots$
These numbers can be expressed as multiples of $7$:
$35 = 7 \times 5$
$49 = 7 \times 7$
$63 = 7 \times 9$
$77 = 7 \times 11$
The multipliers are consecutive odd numbers: $5, 7, 9, 11, \dots$
The next odd number is $13$.
Therefore,the next term is $7 \times 13 = 91$.

(B) The given series is $46, 52, 60, 70, ?$.
Calculate the differences between consecutive terms:
$52 - 46 = 6$
$60 - 52 = 8$
$70 - 60 = 10$
The differences are increasing by $2$ $(6, 8, 10, ...)$.
The next difference should be $10 + 2 = 12$.
Therefore,the next term is $70 + 12 = 82$.

(D) The given series is $1, 11, 111, 1111, \dots$
This is a pattern where the digit $1$ is repeated $n$ times for the $n^{th}$ term.
Term $1$: $1$
Term $2$: $11$
Term $3$: $111$
Term $4$: $1111$
Following this pattern,the $5^{th}$ term will be $11111$.

(D) The pattern followed in the series is:
$\frac{1015 + 1}{2} = 508$
$\frac{508 + 2}{2} = 255$
$\frac{255 + 3}{2} = 129$
$\frac{129 + 4}{2} = 66.5$
Following this logic,the next term is:
$\frac{66.5 + 5}{2} = \frac{71.5}{2} = 35.75$

(C) The pattern follows the rule: $(n \times x) + x$,where $x$ increases by $1$ starting from $2$.
$4 \times 2 + 2 = 10$
$10 \times 3 + 3 = 33$
$33 \times 4 + 4 = 136$
$136 \times 5 + 5 = 685$
$685 \times 6 + 6 = 4110 + 6 = 4116$
Thus,the next number in the series is $4116$.

(B) The given series is $1, 9, 25, 49, ?, 121$.
These numbers can be written as squares of consecutive odd numbers:
$1^2 = 1$
$3^2 = 9$
$5^2 = 25$
$7^2 = 49$
$9^2 = 81$
$11^2 = 121$
Therefore,the missing number is $9^2 = 81$.

(C) The pattern in the series is based on the addition of consecutive odd numbers starting from $3$.
$7 - 4 = 3$
$12 - 7 = 5$
$19 - 12 = 7$
$28 - 19 = 9$
Following this pattern,the next difference should be $11$.
Therefore,the next number is $28 + 11 = 39$.

(C) The given series follows a repeating pattern of adding $2$ and $4$ alternately.
$11 + 2 = 13$
$13 + 4 = 17$
$17 + 2 = 19$
$19 + 4 = 23$
$23 + 2 = 25$
Following this pattern,the next step is to add $4$ to the last number:
$25 + 4 = 29$
Therefore,the missing number is $29$.

(A) The pattern of the series is based on the addition of multiples of $3$ to the difference between consecutive terms.
Step $1$: $12 - 6 = 6$
Step $2$: $21 - 12 = 9$
Step $3$: The next difference should be $9 + 3 = 12$.
Step $4$: Adding $12$ to the last term,we get $21 + 12 = 33$.
Step $5$: To verify,the next difference should be $12 + 3 = 15$. Adding $15$ to $33$ gives $33 + 15 = 48$,which matches the final term in the series.
Therefore,the missing number is $33$.

(A) The pattern in the series is an increasing difference between consecutive terms:
$5 - 2 = 3$
$9 - 5 = 4$
Following this pattern,the next difference should be $5$.
So,the missing term is $9 + 5 = 14$.
To verify,the next difference should be $6$: $14 + 6 = 20$ (which matches the series).
Finally,$20 + 7 = 27$ (which also matches).
Therefore,the missing number is $14$.

(C) The pattern in the series is as follows:
$11 - 6 = 5$
$21 - 11 = 10$
$36 - 21 = 15$
$56 - 36 = 20$
The differences are increasing by $5$ $(5, 10, 15, 20, ...)$.
Therefore,the next difference should be $20 + 5 = 25$.
Adding this to the last term: $56 + 25 = 81$.

(D) Analyze the differences between consecutive terms:
$18 - 10 = 8$
$28 - 18 = 10$
$40 - 28 = 12$
$54 - 40 = 14$
$70 - 54 = 16$
The differences are increasing by $2$ each time $(8, 10, 12, 14, 16)$.
The next difference should be $16 + 2 = 18$.
Therefore,the next term is $70 + 18 = 88$.

(A) The pattern in the series is determined by calculating the difference between consecutive terms:
$120 - 99 = 21$
$99 - 80 = 19$
$80 - 63 = 17$
$63 - 48 = 15$
Notice that the differences are consecutive odd numbers in decreasing order: $21, 19, 17, 15$. The next difference should be $13$.
Therefore,the next term is $48 - 13 = 35$.

(A) The series follows the pattern of adding powers of $2$ to each consecutive term:
$22 + 2^1 = 22 + 2 = 24$
$24 + 2^2 = 24 + 4 = 28$
$28 + 2^3 = 28 + 8 = 36$
$36 + 2^4 = 36 + 16 = 52$
$52 + 2^5 = 52 + 32 = 84$
Therefore,the missing number is $36$.

(A) The pattern in the given series is based on the subtraction of consecutive multiples of $5$ starting from $45$.
Step $1$: $125 - 45 = 80$
Step $2$: $80 - 35 = 45$
Step $3$: $45 - 25 = 20$
Step $4$: $20 - 15 = 5$
Following this pattern of subtracting $45, 35, 25, 15$,the next number is $5$.

(C) Observe the differences between consecutive terms:
$5 - 1 = 4$
$13 - 5 = 8$
$25 - 13 = 12$
$41 - 25 = 16$
The differences are multiples of $4$: $4, 8, 12, 16, ...$
The next difference should be $16 + 4 = 20$.
Therefore,the next term is $41 + 20 = 61$.

(D) The pattern follows the addition of multiples of $13$ to the previous term.
$2 + (13 \times 1) = 15$
$15 + (13 \times 2) = 41$
$41 + (13 \times 3) = 80$
$80 + (13 \times 4) = 132$
Therefore,the next number is $132$.

(D) The given series is $1, 2, 5, 10, 17, ?$.
Observe the pattern:
$0^2 + 1 = 1$
$1^2 + 1 = 2$
$2^2 + 1 = 5$
$3^2 + 1 = 10$
$4^2 + 1 = 17$
Following this pattern,the next term is:
$5^2 + 1 = 25 + 1 = 26$.
Therefore,the missing number is $26$.

(B) The given series consists of the squares of consecutive prime numbers.
$2^{2} = 4$
$3^{2} = 9$
$5^{2} = 25$
$7^{2} = 49$
$11^{2} = 121$
The next prime number after $11$ is $13$.
Therefore,the next term is $13^{2} = 169$.

(C) The given series is $34, 36, 40, 48, 64, ?$.
Observe the differences between consecutive terms:
$36 - 34 = 2 = 2^1$
$40 - 36 = 4 = 2^2$
$48 - 40 = 8 = 2^3$
$64 - 48 = 16 = 2^4$
The pattern of differences is $2^1, 2^2, 2^3, 2^4, \dots$
Following this pattern,the next difference should be $2^5 = 32$.
Therefore,the next term is $64 + 32 = 96$.

(B) The pattern followed in the series is:
$9 \times 2 + 1 = 19$
$19 \times 2 + 2 = 40$
$40 \times 2 + 3 = 83$
$83 \times 2 + 4 = 170$
$170 \times 2 + 5 = 345$
Following this pattern,the next term is:
$345 \times 2 + 6 = 690 + 6 = 696$

(D) The pattern follows the rule: $x_{n+1} = (x_n \div 2) - 6$.
$980 \div 2 - 6 = 490 - 6 = 484$
$484 \div 2 - 6 = 242 - 6 = 236$
$236 \div 2 - 6 = 118 - 6 = 112$
$112 \div 2 - 6 = 56 - 6 = 50$
$50 \div 2 - 6 = 25 - 6 = 19$
Thus,the next number in the series is $19$.

(C) The pattern follows the rule: $(n \times \text{position}) + \text{position}$.
$8 \times 1 + 1 = 9$
$9 \times 2 + 2 = 20$
$20 \times 3 + 3 = 63$
$63 \times 4 + 4 = 256$
$256 \times 5 + 5 = 1285$
Following this logic, the next term is:
$1285 \times 6 + 6 = 7710 + 6 = 7716$.

(C) The given series is $4832, 5840, 6848, ?$.
Calculate the difference between consecutive terms:
$5840 - 4832 = 1008$
$6848 - 5840 = 1008$
Since the difference is constant,the next term is obtained by adding $1008$ to the last term:
$6848 + 1008 = 7856$
Therefore,the missing number is $7856$.

(D) The pattern of the series is as follows:
$10 + 90 = 100$
$100 + 100 = 200$
$200 + 110 = 310$
Following this pattern,the next increment should be $120$.
$310 + 120 = 430$
Therefore,the next number in the series is $430$.

(C) The pattern follows the addition of multiples of $11$ to each consecutive term:
$6 + 11 = 17$
$17 + 22 = 39$
$39 + 33 = 72$
Following this pattern,the next term is $72 + 44 = 116$.

(A) The given series is $325, 259, 204, 160, 127, 105, ?$.
Let us observe the differences between consecutive terms:
$325 - 259 = 66$
$259 - 204 = 55$
$204 - 160 = 44$
$160 - 127 = 33$
$127 - 105 = 22$
The differences are decreasing by $11$ each time $(66, 55, 44, 33, 22, ...)$.
Following this pattern,the next difference should be $22 - 11 = 11$.
Therefore,the next term is $105 - 11 = 94$.