Question

Write the next two terms of the A.P.: `sqrt(27), sqrt(48), sqrt(75)`......

Answer 1

Given A.P. is `sqrt(27), sqrt(48), sqrt(75)` ......

Here, a₁ = `sqrt(27) = 3sqrt(3)`

a₂ = `sqrt(48) = 4sqrt(3)`

∴ Common difference = `4sqrt(3) - 3sqrt(3)`

= `sqrt(3) (4 - 3) = sqrt(3)`

Now, Given a₃ = `sqrt(75) = 5sqrt(3)`

∴ a₄ = `6sqrt(3) = sqrt(108)`

And a₅ = `7sqrt(3) = sqrt(147)`

Hence, next two terms are `sqrt(108)` and `sqrt(147)`.