Question

Find:

the 18^th  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), 3 sqrt(2) ,5  sqrt(2) ,7  sqrt(2),.........`
First term, a =`sqrt(2)`

Common difference, d = 3  `sqrt(2)  - sqrt(2)  = 2  sqrt(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 2 sqrt(2) = sqrt(2) = sqrt(2) + 34 sqrt(2) = 35 sqrt(2) = sqrt(2450) `