Q) Which of the following are APs? If they form an AP, find the common difference d and write three more terms.
(vi) 0.2, 0.22, 0.222, 0.2222, …
Step 1: By observation, we have following terms in the given sequence:
First term, a1 = 0.2, Second term, a2 = 0.22, Third term, a3 = 0.222,
Step 2: Since in an AP, the common difference d is always same between any two consecutive terms, therefore we will calculate difference between 2nd and 1st term also between 3rd term and 2nd term. Then we will check if they are equal or not.
∴ d = a2 – a1 = 0.22 – 0.2 = 0.02
and d = a3 – a2 = 0.222 – 0.22 = 0.002
Since both differences (a2 – a1) and (a3 – a2) are 
equal, hence the given sequence is not an AP.
Therefore, the given sequence is not an AP.
Please do press “Heart” button if you liked the solution