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, …

Ans: Here we are given a sequence and we need to determine if the sequence qualifies to be an AP or not. After that, we need to find the common difference d and next 3 terms (after the given 4 terms).

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 \neq equal, hence the given sequence is not an AP.

Therefore, the given sequence is not an AP.

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