Which of the following are APs? If they form an AP, find the common difference $d$ and write three more terms.
$-\frac{1}{2}, -\frac{1}{2}, -\frac{1}{2}, -\frac{1}{2}, …….$
Given:
Given sequence is $-\frac{1}{2}, -\frac{1}{2}, -\frac{1}{2}, -\frac{1}{2}, …….$
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,
$a_1=-\frac{1}{2}, a_2=-\frac{1}{2}, a_3=-\frac{1}{2}$
$a_2-a_1=-\frac{1}{2}-(-\frac{1}{2})=-\frac{1}{2}+-\frac{1}{2}=0$
$a_3-a_2=-\frac{1}{2}-(-\frac{1}{2})=-\frac{1}{2}+-\frac{1}{2}=0$
$a_2 - a_1 = a_3 - a_2$
$d=a_2 - a_1=-\frac{1}{2}$
$a_5=a_4+d=-\frac{1}{2}+0=-\frac{1}{2}$
$a_6=a_5+d=-\frac{1}{2}+0=-\frac{1}{2}$
$a_7=a_6+d=-\frac{1}{2}+0=-\frac{1}{2}$ 
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