Find out the odd number from the given sequen | vedclass

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Question

(A) Let us analyze the given sequence: $0, 9, 64, 169, 576, 1225$.These numbers can be expressed as squares of the form $(n^2 - 1)^2$ for $n = 1, 2, 3

Vedclass · Accepted Answer

$225$

Vedclass · Answer

(A) Let us analyze the given sequence: $0, 9, 64, 169, 576, 1225$.These numbers can be expressed as squares of the form $(n^2 - 1)^2$ for $n = 1, 2, 3, 4, 5, 6$:For $n=1: (1^2 - 1)^2 = 0^2 = 0$For $n=2: (2^2 - 1)^2 = 3^2 = 9$For $n=3: (3^2 - 1)^2 = 8^2 = 64$For $n=4: (4^2 - 1)^2 = 15^2 = 225$For $n=5: (5^2 - 1)^2 = 24^2 = 576$For $n=6: (6^2 - 1)^2 = 35^2 = 1225$The sequence should be $0, 9, 64, 225, 576, 1225$. The number $169$ is incorrect as it does not fit the pattern $(n^2 - 1)^2$. Replacing $169$ with $225$ makes the series consistent. Thus,$169$ is the odd one out,and $225$ is the correct term that should have been there. Therefore,option $(A)$ is the correct answer.

Find out the odd number from the given sequence: $0, 9, 64, 169, 576, 1225$.

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$\frac{2}{3}, \quad \frac{4}{7}, \quad ?, \quad \frac{11}{21}, \quad \frac{16}{31}$

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