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

√2, √8, √18, √32

He above series can be re written as

√2, √8, √18, √32

⇒ √2, √(2² × 2), √(3² × 2), √(4² × 2)

√2, 2√2, 3√2, 4√2,…..

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

Equal.

d₁ = second term – first term = 2√2 – √2 = √2

d₂ = Third term - Second term = 3√2 – 2√2 =

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(√2) = 5√2 = √50

6^th term is a + (6-1)d = a + 5d = √2 + 5(√2) = 6√2 = √72

7^th term is a + (7-1)d = a + 6d = √2 + 6(√2) = 7√2 = √98.