**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, a_{1 }= 0.2, Second term, a_{2 }= 0.22, Third term, a_{3 }= 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 2^{nd} and 1^{st} term also between 3^{rd} term and 2^{nd} term. Then we will check if they are equal or not.

∴ d = a_{2} – a_{1} = 0.22 – 0.2 = 0.02

and d = a_{3} – a_{2} = 0.222 – 0.22 = 0.002

Since both differences (a_{2 }– a_{1}) and (a_{3 }– a_{2}) 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**