Chapter 9.1, Problem 1QR

To determine

To find: The first four terms and the 30^th term of the sequence.

Answer to Problem 1QR

The first four terms and 30^th term are $u_1=\frac{4}{3},u_2=1,u_3=\frac{4}{5},u_4=\frac{2}{3}\text{and}{u}_{30}=\frac{1}{8}$ respectively.

Explanation of Solution

Given information: $u_n=\frac{4}{n+2}$ .

Concept used: Any term of the sequence can be determined by substituting that term in the sequence.

Calculation:

Substitute $n=1$ into the given sequence and simplify it to determine the first term of the sequence.

  $\begin{array}{c}{u}_1=\frac{4}{1+2}\\ =\frac{4}{3}\end{array}$

Substitute $n=2$ into the given sequence and simplify it to determine the second term of the sequence.

  $\begin{array}{c}{u}_2=\frac{4}{2+2}\\ =1\end{array}$

Substitute $n=3$ into the given sequence and simplify it to determine the first term of the sequence.

  $\begin{array}{c}{u}_3=\frac{4}{3+2}\\ =\frac{4}{5}\end{array}$

Substitute $n=4$ into the given sequence and simplify it to determine the first term of the sequence.

  $\begin{array}{c}{u}_4=\frac{4}{4+2}\\ =\frac{2}{3}\end{array}$

Substitute $n=30$ into the given sequence and simplify it to determine the first term of the sequence.

  $\begin{array}{c}{u}_{30}=\frac{4}{30+2}\\ =\frac{1}{8}\end{array}$