Chapter 12.3, Problem 2E

To determine

To fill: The statement “The sequence given by $a_n=a{r}^{n-1}$ is a geometric sequence in which a is the first term and r is the ________. So, for the geometric sequence $a_n=2{\left(5\right)}^{n-1}$ the first term is _____.”

Answer to Problem 2E

The sequence given by $a_n=a{r}^{n-1}$ is a geometric sequence in which a is the first term and r is the common ratio. So, for the geometric sequence $a_n=2{\left(5\right)}^{n-1}$ the first term is 2.

Explanation of Solution

The terms of the geometric sequence are, $a,ar,a{r}^2,a{r}^3,\cdots$.

The general term of the geometric sequence is $a_n=a{r}^{n-1}$ in which a is the first term and r is the common ratio.

Thus, the first term of the geometric sequence $a_n=2{\left(5\right)}^{n-1}$ is 2.