Question

Find the ninth term of the G.P. 3, 6, 12, 24, ...

Answer 1

In the given G.P., we have the first term, i.e., a = t₁ = 3, and the common ratio, i.e., $r=\frac{t_2}{t_1}=\frac{6}{3}=2$.
We know that the n^th term of the G.P. is t_n = ar^{n – 1}.
By taking a = 3, r = 2 and n = 9, we get:
t₉ = (3)(2)^{9 – 1}
$\Rightarrow$ t₉ = (3)(2)⁸
$\Rightarrow$ t₉ = 3 × 256 = 768
Thus, the 9^th term of the given G.P. is 768.