Chapter 9.8, Problem 41HP

To determine

To evaluate: the geometric sequence that common ratio of $\frac{3}{4}$ .

Answer to Problem 41HP

The sequence becomes $4,3,\frac{9}{4},\mathrm{......}$ .

Explanation of Solution

Given:

The common ratio is given as $\frac{3}{4}$ .

The n^th term of the geometric sequence is given by

  $T_n=a{r}^{n-1}$

Let the first term be 4.

So,

The 1^st term is,

  $\begin{array}{c}{T}_n=a{r}^{n-1}\\ =4{\left(\frac{3}{4}\right)}^0\\ =4\end{array}$

The 2^nd term is,

  $\begin{array}{c}{T}_n=a{r}^{n-1}\\ =4{\left(\frac{3}{4}\right)}^1\\ =3\end{array}$

The 3^rd term is,

  $\begin{array}{c}{T}_n=a{r}^{n-1}\\ =4{\left(\frac{3}{4}\right)}^2\\ =\frac{9}{4}\end{array}$

So, the sequence becomes $4,3,\frac{9}{4},\mathrm{......}$ .