A sequence is given by an=n2−1, n∈N it is not an A.P., then write the sequence

an=n2−1Put n=1, 2, 3, 4, ⋯a1=12−1=−1=0a2=(2)2−1=4−1=3a3=(3)2−1=9−1=8a4=(4)2−1=16−1=15∴ Sequence =0, 3, 8, 15, ⋯

A sequence is given by an=n2−1, n∈N it is not an A.P., then write the sequence

an=n2−1Put n=1, 2, 3, 4, ⋯a1=12−1=−1=0a2=(2)2−1=4−1=3a3=(3)2−1=9−1=8a4=(4)2−1=16−1=15∴ Sequence =0, 3, 8, 15, ⋯

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A sequence is given by $a_{n} = n^{2} - 1, n \in N$ it is not an A.P., then write the sequence

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0, 2, 4, 6, 8, ...

0, 3, 8, 15, ...

0, 3, 6, 9, ....

0, 5, 8, 15, ....

answer is A.

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Detailed Solution

$a_{n} = n^{2} - 1$

Put $n = 1, 2, 3, 4, \dots$

$a_{1} = 1^{2} - 1 = - 1 = 0$

$a_{2} = {(2)}^{2} - 1 = 4 - 1 = 3$

$a_{3} = {(3)}^{2} - 1 = 9 - 1 = 8$

$a_{4} = {(4)}^{2} - 1 = 16 - 1 = 15$

$∴$ Sequence $= 0, 3, 8, 15, \dots$

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A sequence is given by an=n2−1, n∈N it is not an A.P., then write the sequence

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A sequence is given by $a_{n} = n^{2} - 1, n \in N$ it is not an A.P., then write the sequence