Question

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

Answer 1

8th term

Explanation:

Consider the standard geometric sequence :

a , ar , `ar^2 , ar^3 , ar^4 ,...................... , ar^(n-1)`

the nth term = `ar^(n-1)`

here a = 3 (1st term ) , `r = 6/3 = 12/6 =.....= a^n/a^(n-1) = 2`

want to find n where nth term = 384

solve : `ar^(n-1) = 384 rArr 3(2)^(n-1) = 384`

hence `2^(n-1) = 384/3 = 128`

now `2^(n-1) = 2^7 rArr n-1 = 7 rArr n = 8`