Fill in the blank space for the given series | vedclass

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Question

(D) The given series is $5, 17, 37, 65, (\ldots), 145$.We can observe the pattern as follows:$5 = 2^{2} + 1$$17 = 4^{2} + 1$$37 = 6^{2} + 1$$65 = 8^{2

Vedclass · Accepted Answer

$101$

Vedclass · Answer

(D) The given series is $5, 17, 37, 65, (\ldots), 145$.We can observe the pattern as follows:$5 = 2^{2} + 1$$17 = 4^{2} + 1$$37 = 6^{2} + 1$$65 = 8^{2} + 1$The pattern follows the form $n^{2} + 1$ where $n$ is an even number starting from $2$.Following this pattern,the next term should be $10^{2} + 1$.$10^{2} + 1 = 100 + 1 = 101$.The term after that is $12^{2} + 1 = 144 + 1 = 145$,which matches the last term of the series.Therefore,the missing number is $101$.

Fill in the blank space for the given series with the correct alternative.
$5, 17, 37, 65, (\ldots), 145$

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Fill in the blank space for the given series with the correct alternative.$5, 17, 37, 65, (\ldots), 145$