Chapter 12.3, Problem 29AYU

To determine

To find: The $8th$ term of the geometric sequence.

Answer to Problem 29AYU

The $8th$ term of the sequence is $0.00000004$ .

Explanation of Solution

Given information:

The sequence is $0.4,0.04,\mathrm{0.004.......}$ .

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.

  $\begin{array}{c}r=\frac{a_2}{a_1}\\ =\frac{0.04}{0.4}\\ =0.1\end{array}$

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

  $a_n=a_1{r}^{n-1}$

Calculate the fifth term.

  $\begin{array}{c}{a}_8=\left(0.4\right){\left(0.1\right)}^{8-1}\\ =\left(0.4\right){\left(0.1\right)}^7\\ =0.00000004\end{array}$

Therefore, the $8th$ term of the sequence is $0.00000004$ .