Question

Find the next three terms of the sequence :

`sqrt5, 5, 5sqrt(5), .............`

Answer 1

Given sequence: `sqrt5, 5, 5sqrt(5), .............`

Now,

`5/sqrt5 = sqrt5, (5sqrt5)/5 = sqrt(5)`

Since `5/sqrt5 = (5sqrt5)/52 = .......... = sqrt(5)`, the given sequence is a G.P. with first term, a = `sqrt(5)` and common ratio, r = `sqrt(5)`

Now, T_n = ar^{n – 1}

∴ Next three term:

4^th term = `sqrt(5) xx (sqrt5)^3`

= `sqrt(5) xx 5sqrt(5)`

= 25

5^th term = `sqrt(5) xx (sqrt5)^4`

= `sqrt(5) xx 25`

= `25sqrt(5)`

6^th term = `sqrt(5) xx (sqrt5)^5`

= `sqrt(5) xx 25sqrt(5)`

= 125