Chapter 8, Problem 50RE

To determine

To determine the first five terms of the Geometric sequence-

  $a_1=2,r=\frac{3}{2}$

Answer to Problem 50RE

Thefirst five terms of the Geometric Sequence are $2,3,\frac{9}{2},\frac{27}{4},\frac{81}{8}$ .

Explanation of Solution

Given:

Sequence - $a_1=2,r=\frac{3}{2}$

Formula Used:

  $nth$ term of the Geometric sequence is given as $t_n=a{r}^{n-1}$

Calculation:

Given sequence: $a_1=2,r=\frac{3}{2}$

  $\begin{array}{l}{t}_1=2{\left(\frac{3}{2}\right)}^{1-1}\\ t_1=2\end{array}$

  $\begin{array}{l}{t}_2=2{\left(\frac{3}{2}\right)}^{2-1}\\ t_2=2\left(\frac{3}{2}\right)\\ t_2=3\end{array}$

  $\begin{array}{l}{t}_3=2{\left(\frac{3}{2}\right)}^{3-1}\\ t_3=2\left(\frac{9}{4}\right)\\ t_3=\frac{9}{2}\end{array}$

  $\begin{array}{l}{t}_4=2{\left(\frac{3}{2}\right)}^{4-1}\\ t_4=2\left(\frac{27}{8}\right)\\ t_4=\frac{27}{4}\end{array}$

  $\begin{array}{l}{t}_5=2{\left(\frac{3}{2}\right)}^{5-1}\\ t_5=2\left(\frac{81}{16}\right)\\ t_5=\frac{81}{8}\end{array}$

The first five terms of the Geometric Sequence are $2,3,\frac{9}{2},\frac{27}{4},\frac{81}{8}$ .

Conclusion:

Hence, the first five terms of the Geometric Sequence are $2,3,\frac{9}{2},\frac{27}{4},\frac{81}{8}$ .