# Given 3, 6, 12, 24,..., which term number is 384?

Mar 7, 2016

8th term

#### Explanation:

Consider the standard geometric sequence :

a , ar , $a {r}^{2} , a {r}^{3} , a {r}^{4} , \ldots \ldots \ldots \ldots \ldots \ldots \ldots . , a {r}^{n - 1}$

the nth term = $a {r}^{n - 1}$

here a = 3 (1st term ) , $r = \frac{6}{3} = \frac{12}{6} = \ldots . . = {a}^{n} / {a}^{n - 1} = 2$

want to find n where nth term = 384

solve : $a {r}^{n - 1} = 384 \Rightarrow 3 {\left(2\right)}^{n - 1} = 384$

hence ${2}^{n - 1} = \frac{384}{3} = 128$

now ${2}^{n - 1} = {2}^{7} \Rightarrow n - 1 = 7 \Rightarrow n = 8$