Find out the odd number from the given sequen | vedclass

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Question

(D) Let us analyze the differences between consecutive terms in the sequence: $7, 9, 17, 42, 91, 172, 293$.$9 - 7 = 2$$17 - 9 = 8$$42 - 17 = 25$$91 -

Vedclass · Accepted Answer

$9$

Vedclass · Answer

(D) Let us analyze the differences between consecutive terms in the sequence: $7, 9, 17, 42, 91, 172, 293$.$9 - 7 = 2$$17 - 9 = 8$$42 - 17 = 25$$91 - 42 = 49$$172 - 91 = 81$$293 - 172 = 121$The differences are $2, 8, 25, 49, 81, 121$. We observe that $49 = 7^2$,$81 = 9^2$,and $121 = 11^2$. The pattern of differences should be squares of odd numbers: $1^2, 3^2, 5^2, 7^2, 9^2, 11^2$,which are $1, 9, 25, 49, 81, 121$.If the first term is $8$ instead of $7$,the sequence becomes $8, 9, 18, 43, 92, 173, 294$. However,looking at the original sequence $7, 9, 17, 42, 91, 172, 293$,the term $9$ is the odd one out because replacing it with $8$ makes the differences $1^2, 3^2, 5^2, 7^2, 9^2, 11^2$. Thus,$9$ is the incorrect term.

Find out the odd number from the given sequence: $7, 9, 17, 42, 91, 172, 293$.

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