Question

Question 4 (xv)
Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
(xv) $1^2,5^2,7^2,73,\dots$

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 :
$1^2,5^2,7^2,73,\dots$
$i.e,1,25,49,73,...$
Here,
$a_2-a_1=25-1=24a_3-a_2=49-25=24a_4-a_3=73-49=24$

Note that the difference between any two consecutive terms of the series is a constant value.
Therefore,d =24 and the given numbers are in A.P.

Next three terms are:
$a_5=73+24=97a_6=97+24=121a_7=121+24=145$