Question

Find the seventh term of the G.P. :

`1, sqrt(3), 3, 3sqrt(3), ............`

Answer 1

Given G.P. `1, sqrt(3), 3, 3sqrt(3), ............`

Here,

First term, a = 1

Common ratio, r = `sqrt(3)/1 = sqrt(3)`

Now, T_n = ar^{n – 1}

`\implies` T₇ = `1 xx (sqrt(3))^(7 - 1)`

= `1 xx (sqrt(3))^6`

= `(sqrt(3))^6`

= `sqrt(3) xx sqrt(3) xx sqrt(3) xx sqrt(3) xx sqrt(3) xx sqrt(3)`

= 3 × 3 × 3

= 27