Find the odd number in the given sequence: 32 | vedclass

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Question

(A) Let us analyze the differences between consecutive terms in the sequence: $34 - 32 = 2$ $37 - 34 = 3$ $46 - 37 = 9$ $62 - 46 = 16$ $87 - 62 = 25$

Vedclass · Accepted Answer

$34$

Vedclass · Answer

(A) Let us analyze the differences between consecutive terms in the sequence: $34 - 32 = 2$ $37 - 34 = 3$ $46 - 37 = 9$ $62 - 46 = 16$ $87 - 62 = 25$ $123 - 87 = 36$ Observing the differences: $2, 3, 9, 16, 25, 36$. We can see that $9, 16, 25, 36$ are squares of $3^2, 4^2, 5^2, 6^2$ respectively. To maintain this pattern,the first two differences should be $1^2 = 1$ and $2^2 = 4$. If we replace $34$ with $33$,the sequence becomes $32, 33, 37, 46, 62, 87, 123$. The differences would then be: $33 - 32 = 1 = 1^2$ $37 - 33 = 4 = 2^2$ $46 - 37 = 9 = 3^2$ $62 - 46 = 16 = 4^2$ $87 - 62 = 25 = 5^2$ $123 - 87 = 36 = 6^2$ Thus,the odd number in the sequence is $34$.

Find the odd number in the given sequence: $32, 34, 37, 46, 62, 87, 123$.

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