Fill in the blank space for the given series | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let us analyze the pattern of the given series: $0, 2, 8, 14, (. . .), 34$.The differences between consecutive terms are:$2 - 0 = 2$$8 - 2 = 6$$14

Vedclass · Accepted Answer

$24$

Vedclass · Answer

(A) Let us analyze the pattern of the given series: $0, 2, 8, 14, (. . .), 34$.The differences between consecutive terms are:$2 - 0 = 2$$8 - 2 = 6$$14 - 8 = 6$This does not show a simple arithmetic progression. Let us look at the terms again:$0 = 1^2 - 1$$2 = 2^2 - 2$$8 = 3^2 - 1$$14 = 4^2 - 2$The pattern follows alternating subtractions of $1$ and $2$ from the squares of consecutive integers ($n^2 - 1$ for odd $n$,$n^2 - 2$ for even $n$).Following this pattern,the next term $(n=5)$ should be $5^2 - 1 = 25 - 1 = 24$.Checking the next term $(n=6)$: $6^2 - 2 = 36 - 2 = 34$,which matches the series.Therefore,the missing number is $24$.

Fill in the blank space for the given series with the correct alternative: $0, 2, 8, 14, (. . .), 34$

Similar Questions

Choose the correct alternative to complete the series: $c _ a c _ a a _ a a _ b e _ b c c$

Choose the correct alternative to complete the series: $b . . b . . b b . . . b b b . . . . b b . . b$

Choose the correct alternative for the missing terms in the series: $Y, W, U, S, Q, ?, ?$

Find the missing letters for the given series from the given alternatives:
$.....bca......cca....ca.....b.....c$

Fill in the blank space for the given series with the correct alternative.
$1, 4, 9, 16, 25, (\ldots)$

Vedclass Test Series

Exam Paper Generator

Online Exam Module