Question

A geometric sequence is defined by the equation an = (4)3 − n. What are the first three terms of the sequence and what is the common ratio, r?

Answer 1

$x_{n} = 4^{3-n} , x_{1} =4^{3-1}=4^{2}=16 x_{2}=4^{3-2}=4^{1}=4 x_{3}= 4^{3-3}= 4^{0} =1 Common ratio = x_{3}/x_{2}= \frac{1}{4}$