Question

Question 4 (xiv)
Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
(xiv) $1^2,3^2,5^2,7^2,\dots$

Answer 1

If the difference between any two consecutive terms of a series is a constant value, then the series is an A.P.

Given, the series is :
$1^2,3^2,5^2,7^2,\dots$
Or, $1,9,25,\mathrm{49....}$
Here,
$a_2-a_1=9-1=8a_3-a_2=25-9=16a_4-a_3=49-25=24$

Note that the difference between any two consecutive terms of the series is not a constant value.
Hence, the given series is not an AP.