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

2, 5/2, 3, 7/2

For a series to be in AP, the common difference (d) should be

Equal.

d₁ = second term – first term = – 2 = 0.5

d₂ = Third term - Second term = 3 – = 0.5

Since common difference is same the above series is in AP.

The next three terms will be the 5^th, 6^th, 7^th.

5^th term will be given by = a + (5-1)d = a + 4d = 2 + 4(0.5) = 4

6^th term is a + (6-1)d = a + 5d = 2 + 5(0.5) = 4.5

7^th term is a + (7-1)d = a + 6d = 2 + 6(0.5) = 5.