Question

Following are APs or not? If they form an A.P. find the common difference d and write three more terms: 

 `sqrt2, sqrt8, sqrt18, sqrt32 ...`

Answer 1

`sqrt2, sqrt8, sqrt18, sqrt32 ...`

Here,

a₂ - a₁ = `sqrt8 - sqrt2 = 2sqrt2 - sqrt2 = sqrt2`

a₃ - a₂ = `sqrt18 - sqrt8 = 3sqrt2 - 2sqrt2 = sqrt2`

a₄ - a₃ = `4sqrt2 - 3sqrt2 = sqrt2`

⇒ a_n+1 - a_n is same every time.

Therefore, `d = sqrt2` and the given numbers are in A.P.

Three more terms are

a₅ = `sqrt32 + sqrt2 = 4sqrt2 + sqrt2 = 5sqrt2 = sqrt50`

a₆ = `5sqrt2 +sqrt2 = 6sqrt2 = sqrt72`

a₇ = `6sqrt2 + sqrt2 = 7sqrt2 = sqrt98`