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,
$a_1=a, a_2=2a, a_3=3a$
$a_2-a_1=2a-a=a$
$a_3-a_2=3a-2a=a$
$a_2 - a_1 = a_3 - a_2$
$d=a_2 - a_1=a$
$a_5=a_4+d=4a+a=5a$
$a_6=a_5+d=5a+a=6a$
$a_7=a_6+d=6a+a=7a$
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