Question

Which term of the G.P. 5, 10, 20, 40, ..... is 640?

Answer 1

Here the first term $$a = 5$$ and the common ratio $$r = \frac{10}{5} = 2$$.

Let the 640 be the nth term. Then,

$$T_n = ar^{n - 1} \Rightarrow 5 \times 2^{n - 1} = 640$$

$$2^{n - 1} = \frac{640}{5} = 128 = 2^7$$

$$n - 1 = 7 \Rightarrow n = 8$$

Hence, 640 is the 8th term of the given G.P.