Chapter 12.3, Problem 27AYU

To determine

To find: The ninth term of the geometric sequence.

Answer to Problem 27AYU

The ninth term of the sequence is $1$ .

Explanation of Solution

Given information:

The sequence is $1,-1,\mathrm{1.......}$ .

Calculation:

The first term of a sequence is denoted as $a_1$ and the second term of the sequence is denoted by $a_2$ .

Calculate the common ratio.

  $\begin{array}{c}r=\frac{a_2}{a_1}\\ =\frac{-1}{1}\\ =1\end{array}$

The formula for nth term of geometric sequence is given by,

  $a_n=a_1{r}^{n-1}$

Calculate the fifth term.

  $\begin{array}{c}{a}_9=\left(1\right){\left(-1\right)}^{9-1}\\ =\left(1\right){\left(-1\right)}^8\\ =1\end{array}$

Therefore, the ninth term of the sequence is $1$ .