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General Form of an AP

The n th t...

Question

The $n^{t h}$ term of an $A P$ cannot be $n^{2} + 1 .$ Justify the statement.

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Solution

Taking n = 1 is $n^{2} + 1,$ we get
$a_{1} = 1 + 1 = 2$
$a_{2} = 4 + 1 = 5$ for n = 2
$a_{3} = 9 + 1 = 10$ for n = 3
we observe that common difference is not the same
Hence, $n^{t h}$ term of an A,P. can't be $n^{2} + 1$

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