**Q) Which of the following are APs? If they form an AP, find the common difference d and write three more terms. **

**(ii) 2, 5/2 ,3, 7/2, …**

**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 }= 2, Second term, a_{2 }= , Third term, a_{3 }= 3,

**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.

and

Since both differences (a_{2 }– a_{1}) and (a_{3 }– a_{2}) are equal, hence the given sequence is an AP.

**Step 3:** Now since it is confirmed that the given sequence is an AP, we will now calculate its next 3 terms:

Here, first term a_{1} = 2 and common difference, d = ,

We know that the n^{th} term of an AP is given by: a_{n }= a ( n – 1) d

Therefore, 5^{th} term,

Similarly, 6^{th} term,

and, 7^{th} term,

**Therefore, the given sequence is an AP, the common difference is and next 3 terms of this AP are: 4, and 5.**

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