Question

A sequence is given by an=nsquare-1,n=N.Prove that it is not an AP

Answer 1

Answer:

The given sequence is

$aₙ = n² - 1 ...........(1)$

Now

$aₙ₋₁ = (n - 1)² - 1$

$aₙ₋₁ = n² - 2n - 2............(2)$

We know that difference in consecutive terms of a sequence give the common difference(d)

$d = aₙ - aₙ₋₁$

$d = (n² - 1) - (n² - 2n - 2)$

$d = 2n + 1$

It is clear that the difference between the terms is not a constant but depends on value of n. Hence the given sequence is not an AP.