Chapter 7.9, Problem 28PPS

To determine

To find the 15^th term of the given geometric sequence.

Answer to Problem 28PPS

15^th term of the sequence is $-43,046,721$ .

Explanation of Solution

Given:

  $-9,27,-81,\mathrm{.........}$

Concept used:

The n^th term of a geometric sequence with first term ‘a’ and common ratio ‘r’ is

  $a_n=a{r}^{n-1}$

Calculation:

  $-9,27,-81,\mathrm{.........}$

It is a geometric sequence with

  $a=-9\&r=\frac{27}{-9}=-3$

Now the 15^th term is,

  $\begin{array}{l}{a}_{15}=a{r}^{14}\\ \Rightarrow a_{15}=-9{\left(-3\right)}^{14}\\ \Rightarrow a_{15}=-9\left(4782969\right)\\ \Rightarrow a_{15}=-43,046,721\end{array}$