Question

Find the next two terms of the series :

2 – 6 + 18 – 54 ..........

Answer 1

Given series: 2 – 6 + 18 – 54 ............

Now,

`(-6)/2 = -3, 18/(-6) = -3, (-54)/18 = -3`

Since `(-6)/2 = 18/(-6) = (-54)/18 = -3`, the given sequence is a G.P. with first term, a = 2 and common ratio, r = –3.

Now, T_n = ar^{n – 1}

∴ Next two terms:

5^th term = 2 × (–3)⁴

= 2 × 81

= 162

6^th term = 2 × (–3)⁵

= 2 × (–243)

= – 486