Find out the odd number from the given sequen | vedclass

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Question

(A) Let us analyze the differences between consecutive terms in the sequence:$45 - 41 = 4 = 2^2$$61 - 45 = 16 = 4^2$$97 - 61 = 36 = 6^2$$181 - 97 = 84

Vedclass · Accepted Answer

$181$

Vedclass · Answer

(A) Let us analyze the differences between consecutive terms in the sequence:$45 - 41 = 4 = 2^2$$61 - 45 = 16 = 4^2$$97 - 61 = 36 = 6^2$$181 - 97 = 84$ (This is not $8^2 = 64$)$261 - 181 = 80$$405 - 261 = 144 = 12^2$If we follow the pattern of adding squares of even numbers $(2^2, 4^2, 6^2, 8^2, 10^2, 12^2)$:$41 + 4 = 45$$45 + 16 = 61$$61 + 36 = 97$$97 + 64 = 161$$161 + 100 = 261$$261 + 144 = 405$Comparing this with the given sequence,$181$ is the incorrect term and should be $161$.

Find out the odd number from the given sequence: $41, 45, 61, 97, 181, 261, 405$.

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