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

3, 3 + √ 2, 3 + 2√ 2, 3 + 3√ 2 ……

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

Equal.

D₁ = second term – first term = 3 + √ 2 - 3 = √ 2

D₂ = Third term - Second term = 3 + 2√ 2 - 3 + √ 2 = √2

Since common difference is equal 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 = 3 + 4(√2) = 3 + 4√2

6^th term is a + (6-1)d = a + 5d = -10 + 5(√2) = 3 + 5√2

7^th term is a + (7-1)d = a + 6d = -10 + 6(√2) = 3 + 6√2.