Question

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

`sqrt3, sqrt6, sqrt9, sqrt12 ...`

Answer 1

`sqrt3, sqrt6, sqrt9, sqrt12`

Here,

a₂ - a₁ = `sqrt6 - sqrt3 = sqrt3 × 2 -sqrt3 = sqrt3(sqrt2 - 1)`

a₃ - a₂ = `sqrt9 - sqrt6 = 3 - sqrt6 = sqrt3(sqrt3 - sqrt2)`

a₄ - a₃ = `sqrt12 - sqrt9 = 2sqrt3 - sqrt3 × 3 = sqrt3(2 - sqrt3)`

⇒ a_n+1 - a_n is not the same every time.

Therefore, the given numbers do not form an AP.