Chapter 13, Problem 32CCSR

Solution

To explain: How to find the term $\left(a_7\right)$ in a geometric sequence whose first term $a_1=8$ and fourth term $a_4=27$ .

By using the formula for the nth term $\left(a_n\right)=a{r}^{n-1}$ where $\left(n\right)$ is the nth term, ( a ) is the first term and ( r ) is the common ratio of a geometric sequence, first evaluate the common ratio $\left(r\right)$ using the formula for nth term of geometric sequence and then find the seventh term $\left(a_7\right)$ by substituting the parameters like common ratio ( r ), $n=7$ and first term $a_1=8$ . The value of $\left(a_7\right)$ can be found easily in this way.

Given:

The first term $a_1=8$ and fourth term $a_4=27$ of the geometric sequence.

Explanation:

With the help of formula for the nth term $\left(a_n\right)=a{r}^{n-1}$ where $\left(n\right)$ is the nth term, ( a ) is the first term and ( r ) is the common ratio of a geometric sequence, first evaluate the common ratio $\left(r\right)$ using the formula $\left(a_n\right)=a{r}^{n-1}$ for nth term of geometric sequence then find the seventh term $\left(a_7\right)$ by substituting the parameters like common ratio ( r ), $n=7$ and first term $a_1=8$ . The value of $\left(a_7\right)$ can be found easily in this way.