Chapter 9, Problem 1RE

To determine

To write:

The first five terms of the given sequence.

Answer to Problem 1RE

$a_1=-1,a_2=1,a_3=3,a_4=5,a_5=7$

Explanation of Solution

Given information:

The sequence $a_n=2n-3$

Concept used:

To evaluate the terms of a sequence, we substitute the values of n in it and simplify.

Calculation:

In order to find the first five terms of the given sequence, we will substitute $n=1,2,3,4,\text{ and 5}$ in the given sequence and find the corresponding values.

So for $n=1$, we have

$\begin{array}{l}{a}_1=2\left(1\right)-3\\ =2-3\\ =-1\end{array}$

Similarly for $n=2$, we get

$\begin{array}{l}{a}_2=2\left(2\right)-3\\ =4-3\\ =1\end{array}$

For $n=3$, the sequence gives

$\begin{array}{l}{a}_3=2\left(3\right)-3\\ =6-3\\ =3\end{array}$

For $n=4$, we have

$\begin{array}{l}{a}_4=2\left(4\right)-3\\ =8-3\\ =5\end{array}$

And for $n=5$, we have

$\begin{array}{l}{a}_5=2\left(5\right)-3\\ =10-3\\ =7\end{array}$

Thus the first five terms of the given sequence are, $a_1=-1,a_2=1,a_3=3,a_4=5,\text{and}{a}_5=7$.