Chapter 8, Problem 52RE

To determine

To determine the first five terms of the Geometric sequence-

  $a_1=2,a_2=12$

Answer to Problem 52RE

Thefirst five terms of the Geometric Sequence are $2,12,72,432,2592$ .

Explanation of Solution

Given:

Sequence - $a_1=2,a_2=12$

Formula Used:

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

Calculation:

Given sequence: $a_1=2,a_2=12$

Thus, $r=\frac{a_2}{a_1}$

  $\begin{array}{l}r=\frac{12}{2}\\ r=6\end{array}$

  $\begin{array}{l}{a}_3=2{\left(6\right)}^{3-1}\\ a_3=2\left(36\right)\\ a_3=72\end{array}$

  $\begin{array}{l}{a}_4=2{\left(6\right)}^{4-1}\\ a_4=2\left(216\right)\\ a_4=432\end{array}$

  $\begin{array}{l}{a}_5=2{\left(6\right)}^{5-1}\\ a_5=2\left(1296\right)\\ a_5=2592\end{array}$

The first five terms of the Geometric Sequence are $2,12,72,432,2592$ .

Conclusion:

Hence, the first five terms of the Geometric Sequence are $2,12,72,432,2592$ .