## Precalculus: Mathematics for Calculus, 7th Edition

A geometric sequence is a sequence whose terms are obtained by multiplying each term by the same fixed constant $r$ to get the next term. A geometric sequence has the form $a, ar, ar^{2}, ar^{3}, \ldots$ The number $a$ is the first term of the sequence, and the number $r$is the common ratio. The nth term of the sequence is $\quad a_{n}=ar^{n-1}$ -------------- By comparing the general formula for the n-th term, $a=7, r=3.$ a. The first five terms $a_{1}=7$ $a_{2}=7(3)=21$ $a_{3}=21(3)=63$ $a_{4}=63(3)=189$ $a_{5}=189(3)=567$ b. $r=3$ c. graphed in desmos.com (image attached in answer)