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

##### 1 Answer

Mar 7, 2016

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 #