Question

Find the 18th term of the AP `sqrt(2), sqrt(18), sqrt(50), sqrt(98)`,....

Answer 1

The given AP is `sqrt(2), sqrt(18), sqrt(50), sqrt(98)`,....

This can be re-written as `sqrt(2), 3sqrt(2), 5sqrt(2), 7sqrt(2)`,....

First term, a = `sqrt(2)`

Common difference, d = `3sqrt(2) - sqrt(2) = 2sqrt(2)`

n^th term of the AP,

a_n  = a + (n – 1)d

= `sqrt(2) + (n - 1) xx 2 sqrt(2)`

 ∴ 18^th term of the AP,

a₁₈ = `sqrt(2) + (18 - 1) xx 2sqrt(2)`

= `sqrt(2) + 34sqrt(2)`

= `35sqrt(2)`

= `sqrt(2450)`