Chapter 8, Problem 1RE

List all terms of each finite sequence.

a_n = 2^n–1 for 1 ≤= n ≤= 5

To determine

To calculate: The first 5 terms of the sequence $a_n=2^{n-1},1\le n\le 5$.

Answer to Problem 1RE

Solution:

The first 5 terms of the sequence $a_n=2^{n-1},1\le n\le 5$ are $1,2,4,8,16$.

Explanation of Solution

Given:

The n th term of the sequence is $a_n=2^{n-1},1\le n\le 5$

Calculation:

In order to find the terms of the sequence where general term is $a_n=2^{n-1},1\le n\le 5$, substitute the n in the formula with $1,2,3,4,5$ as shown below:

1^st term

$\begin{array}{c}{a}_1=2^{1-1}\\ =1\end{array}$

2^nd term

$\begin{array}{c}{a}_2=2^{2-1}\\ =2\end{array}$

3^rd term

$\begin{array}{c}{a}_3=2^{3-1}\\ =2\times 2\\ =4\end{array}$

4^th term

$\begin{array}{c}{a}_4=2^{4-1}\\ =2\times 2\times 2\\ =8\end{array}$

5^th term

$\begin{array}{c}{a}_5=2^{5-1}\\ =2\times 2\times 2\times 2\\ =16\end{array}$

Hence, the first 5 terms of the sequence $a_n=2^{n-1},1\le n\le 5$ are $1,2,4,8,16$.