Question

Question 4 (viii)
Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
(viii) $-\frac{1}{2},-\frac{1}{2},-\frac{1}{2},-\frac{1}{2}\dots \dots$

Answer 1

(viii)
$-\frac{1}{2},-\frac{1}{2},-\frac{1}{2},-\frac{1}{2}\dots \dots$
Here,
$a_2-a_1=(-\frac{1}{2})-(-\frac{1}{2})=0a_3-a_2=(-\frac{1}{2})-(-\frac{1}{2})=0a_4-a_3=(-\frac{1}{2})-(-\frac{1}{2})=0$
$\Rightarrow a_{n+1}-a_n$ is same everytime.
Therefore,d=0 and the given numbers are in A.P.
Next three terms are:
$a_5=(-\frac{1}{2})-0=-\frac{1}{2}{a}_6=(-\frac{1}{2})-0=-\frac{1}{2}{a}_7=(-\frac{1}{2})-0=-\frac{1}{2}$