The nth term u_n of a geometric sequence is given by u_n = 3(4)^(n+1), n in ZZ^+. What is the common ratio r?

I supposed r might be 4 but the nth term of a geometric sequence is normally given by u_n = u_1*r^(n-1), but in the question 4 has a power of n+1 so I'm confused by n+1 and n-1

1 Answer
Nov 25, 2017

4.

Explanation:

The Common Ratio r of a Geometric Sequence

{u_n=u_1*r^(n-1) : n in ZZ^+} is given by,

r=u_(n+1) -: u_n.............(ast).

Since, u_n=3*4^(n+1), we have, by (ast),

r={3*4^((n+1)+1)}-:{3*4^(n+1)}.

rArr r=4.