Which of the following are APs? If they form an AP, find the common difference $d$ and write three more terms.
$1^2, 5^2, 7^2, 73, ……$

Given:

Given sequence is $1^2, 5^2, 7^2, 73, ……$

To do:

We have to check whether the given sequence is an AP. If it is an AP we have to find the common difference $d$ and write three more terms.

Solution:

In the given sequence,

$a_1=1^2=1, a_2=5^2=25, a_3=7^2=49$

$a_2-a_1=25-1=24$

$a_3-a_2=49-25=24$

$a_2 - a_1 = a_3 - a_2$

$d=a_2 - a_1=24$

$a_5=a_4+d=73+24=97$

$a_6=a_5+d=97+24=121$

$a_7=a_6+d=121+24=145$