Question

The 10^th term of the A.P. `sqrt(2), sqrt(8), sqrt(18), ...` is ______.

Options

• `sqrt(162)`

• `sqrt(200)`

• `sqrt(54)`

• `sqrt(94)`

Answer 1

The 10^th term of the A.P. `sqrt(2), sqrt(8), sqrt(18)`, ... is `underlinebb(sqrt(200))`.

Explanation:

Given A.P.: `sqrt(2), sqrt(8), sqrt(18), ...`

Simplifying the terms:

`a_1 = sqrt(2)`

`a_2 = sqrt(8) = 2sqrt(2)`

`a_3 = sqrt(18) = 3sqrt(2)`

Common difference (d):

`d = 2sqrt(2) - sqrt(2)`

`d = sqrt(2)`

Finding the 10^th term (a₁₀):

a₁₀ = a + (10 – 1)d

`a_10 = sqrt(2) + 9sqrt(2)`

`a_10 = 10sqrt(2)`

`a_10 = sqrt(100 xx 2)`

`a_10 = sqrt(200)`