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

(viii) – 1/2, – 1/2, – 1/2, – 1/2, …

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, a₁ = , Second term, a₂ = , Third term, a₃ =

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 (a₂ – a₁) and (a₃ – a₂) 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 4 terms:

Here, first term a₁ = and common difference, d = 0,

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: , , and .

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