Chapter 14.4, Problem 1PE

a. A ______________sequence is a sequence in which the ratio between each term and its predecessor is constant.

b. The common ____________ between a term and its predecessor in a geometric sequence is often denoted by r.

c. The n th term of a geometric sequence is given by $a_n=\_\_\_\_\_\_\_\_\_\_\_$, where $a_n$ is the n th term in the sequence, $a_1$ is the first term, and r is the common ratio.

d. The sum $S_n$ of the first n terms of a geometric series ${\displaystyle \underset{i=1}{\overset{n}{\sum }}{a}_1{r}^{i-1}}$ is given by $S_n=\_\_\_\_\_\_\_\_\_\_\_\_$, where $a_1$ is the first term and r is the common ratio.

e. Given an infinite geometric series $a_1+a_{2}r+a_1{r}_2+\mathrm{...}$  ?​? with $\left|r\right|<1$, the sum of all terms in the sequence is given by $S=$ ___________. If $\left|r\right|\ge$  ? _________, then the sum does not exist.