Chapter 10, Problem 1RE

In Exercises 1-6, write the first four terms of each sequence whose general term is given.

$a_n=7n-4$

To determine

To Calculate: The first four terms of the sequence whose general term is $a_n=7n-4$.

Answer to Problem 1RE

Solution:

The first four terms of the sequence whose general term is $a_n=7n-4$ are $a_1=3,a_2=10,a_3=17,a_4=24$.

Explanation of Solution

Given Information:

The general term of the sequence is $a_n=7n-4$.

Formula used:

To find the first four terms of the sequence, substitute $n=1,2,3,4$ in the general term $a_n=7n-4$.

Calculation:

Let us consider the provided general term of sequence,

$a_n=7n-4$

For first term, substitute $n=1$,

$\begin{array}{c}{a}_1=7\left(1\right)-4\\ =7-4\\ =3\end{array}$

For second term, put $n=2$,

$\begin{array}{c}{a}_2=7\left(2\right)-4\\ =14-4\\ =10\end{array}$

For third term, substitute $n=3$,

$\begin{array}{c}{a}_3=7\left(3\right)-4\\ =21-4\\ =17\end{array}$

For fourth term, substitute $n=4$,

$\begin{array}{c}{a}_4=7\left(4\right)-4\\ =28-4\\ =24\end{array}$

Therefore, first four terms $a_1,a_2,a_3,a_4$ are $3,10,17,24$ respectively.