Question

Find the common ratio and the 7th term of the G.P. 2, -6, 18, ...

Answer 1

In the given G.P., we have t₁ = 2, t₂ = –6 and t₃ = 18.
Thus, we have the first term, i.e., a = t₁ = 2, and the common ratio, i.e., $r=\frac{t_2}{t_1}=\frac{-6}{2}=-3$.
We know that the n^th term of the G.P. is t_n = ar^{n – 1.}
By taking a = 2, r = –3 and n = 7, we have:
t₇ = (2)(–3)^{7 – 1}
$\Rightarrow$t₇ = (2)(–3)⁶
$\Rightarrow$t₇ = 2 × 729 = 1458
Thus, the common ratio of the given G.P. is –3 and the 7^th term is 1458.