Question

Find the next three terms of the series :

`2/27, 2/9, 2/3, .............`

Answer 1

Given sequence: `2/27, 2/9, 2/3, .............`

Now,

`(2/9)/(2/27) = 3, (2/3)/(2/9) = 3`

Since `(2/9)/(2/27) = (2/3)/(2/9) = .......... = 3`, the given sequence is a G.P. with first term, a = `2/27` and common ratio, r = 3.

Now, T_n = ar^{n – 1}

∴ Next three terms:

4^th term =`2/27xx(3)^3`

= `2/27 xx 27`

= 2

5^th term =`2/27 xx (3)^4`

= `2/27 xx 27 xx 3`

= 6

6^th term = `2/27 xx (3)^5`

= `2/27 xx 27 xx 9`

= 18