Question

Which term of the G.P. 3, 6, 12, 24, ..... is 768?

Answer 1

Here the first term $$a = 3$$ and the common ratio $$r = \frac{6}{3} = 2$$.

Let the 768 be the nth term. Then,

$$T_n = ar^{n - 1} \Rightarrow 3 \times 2^{n - 1} = 768$$

$$2^{n - 1} = \frac{768}{3} = 256 = 2^8$$

$$n - 1 = 8 \Rightarrow n = 9$$

Hence, 768 is the 9th term of the given G.P.