Find the odd number in the given sequence: 6, | vedclass

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Question

(D) Let us analyze the differences between consecutive terms in the sequence: $6, 7, 16, 41, 90, 154, 292$.$7 - 6 = 1 = 1^2$$16 - 7 = 9 = 3^2$$41 - 16

Vedclass · Accepted Answer

$154$

Vedclass · Answer

(D) Let us analyze the differences between consecutive terms in the sequence: $6, 7, 16, 41, 90, 154, 292$.$7 - 6 = 1 = 1^2$$16 - 7 = 9 = 3^2$$41 - 16 = 25 = 5^2$$90 - 41 = 49 = 7^2$$154 - 90 = 64 
eq 81 (9^2)$$292 - 154 = 138 
eq 121 (11^2)$Following the pattern of adding consecutive odd squares $(1^2, 3^2, 5^2, 7^2, 9^2, 11^2)$:$90 + 9^2 = 90 + 81 = 171$$171 + 11^2 = 171 + 121 = 292$Thus,the term $154$ is incorrect and should be $171$.

Find the odd number in the given sequence: $6, 7, 16, 41, 90, 154, 292$.

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