Which of the following are APs? If they form an AP, find the common difference $d$ and write three more terms.
$a, 2a, 3a, 4a, …….$

Given:

Given sequence is $a, 2a, 3a, 4a, …….$

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,

$a_1=a, a_2=2a, a_3=3a$

$a_2-a_1=2a-a=a$

$a_3-a_2=3a-2a=a$

$a_2 - a_1 = a_3 - a_2$

$d=a_2 - a_1=a$

$a_5=a_4+d=4a+a=5a$

$a_6=a_5+d=5a+a=6a$

$a_7=a_6+d=6a+a=7a$