Chapter 8, Problem 1RE

Exercises 1-4, write the first five terms of the sequence. (Assume that $n$ begins with 1.)

$a_n=3+\frac{12}{n}$

To determine

To calculate: The first five terms of the sequence $a_n=3+\frac{12}{n}$.

Answer to Problem 1RE

The first five terms of the sequence $a_n=3+\frac{12}{n}$ are $15,9,7,6$, and $\frac{27}{5}$.

Explanation of Solution

Calculation:

Consider the sequence,

$a_n=3+\frac{12}{n}$

Compute the first five terms of the given sequence as follows:

Calculate the first term by substituting $n=1$,

$\begin{array}{c}{a}_1=3+\frac{12}{1}\\ =3+12\\ =15\end{array}$

Similarly, calculate the second term by substituting $n=2$,

$\begin{array}{c}{a}_2=3+\frac{12}{2}\\ =3+6\\ =9\end{array}$

Calculate the third term by substituting $n=3$,

$\begin{array}{c}{a}_3=3+\frac{12}{3}\\ =3+4\\ =7\end{array}$

Calculate the fourth term by substituting $n=4$,

$\begin{array}{c}{a}_4=3+\frac{12}{4}\\ =3+3\\ =6\end{array}$

Calculate the fifth term by substituting $n=5$,

$\begin{array}{c}{a}_5=3+\frac{12}{5}\\ =\frac{15+12}{5}\\ =\frac{27}{5}\end{array}$

Thus, the first five terms of the sequence $a_n=3+\frac{12}{n}$ are $15,9,7,6$, and $\frac{27}{5}$.