Chapter 7.9, Problem 27PPS

To determine

To Find: The $14th$ term of geometric sequence with first term $2$ and common ratio $4$

Answer to Problem 27PPS

  $a_{14}=134217728$

Explanation of Solution

Given information:

Geometric series first term $2$ and common ratio $4$

Concept and Formula Used:

Geometric Sequence: Sequence in which each term after the first is found by multiplying the previous term by a constant called common ratio.

  $nth$ term of the geometric sequence is $a_n=a{r}^{n-1}$ where ‘a’ is the first term and ‘r’ is the common ratio.

Calculation:

It is given that first term $2$ and common ratio is 4.

  $\begin{array}{l}a=2,r=4\&n=14\\ a_n=a{r}^{n-1}\\ a_{14}=2{\left(4\right)}^{14-1}\\ a_{14}=2{\left(4\right)}^{13}\\ a_{14}=134217728\end{array}$

Conclusion:

  $a_{14}=134217728$