Chapter 8, Problem 20CCSR

To determine

To Find : The seventh term of the given sequence.

Answer to Problem 20CCSR

The seventh term of the given sequence is equal to $\frac{1}{9}$ .

Explanation of Solution

Given information:

The following sequence:

  $81,27,9,3,1,\mathrm{.....}$

The given sequence is a geometric sequence so that the common ratio is calculated as follows,

  $\begin{array}{cc}r& =\frac{27}{81}\\ & =\frac{1}{3}\end{array}$

The seventh term of the above sequence is calculated by the following formula,

  $a_n=a_1{r}^{n-1}$

Put the values of $n,a_1$ and r to calculate seventh term,

  $\begin{array}{l}{a}_7=a_1{r}^{7-1}\\ =81\cdot {\left(\frac{1}{3}\right)}^6\\ =81\cdot \frac{1}{729}\\ =\frac{1}{9}\end{array}$

Hence, the seventh term of the above sequence is equal to $\frac{1}{9}$ .