Chapter 12, Problem 1CT

To determine

To find: The first five terms of each sequence.

Answer to Problem 1CT

The first five terms of the given sequence are $0,\frac{3}{10},\frac{8}{11},\frac{5}{4}$ .and $\frac{24}{13}$ .

Explanation of Solution

Given information:

The given terms are $\left\{s_n\right\}=\left\{\frac{n^2-1}{n+8}\right\}$ .

Calculation:

Substitute $1,2,3,4$ and $5$ for $n$ to get the first five terms in the sequence $\left\{s_n\right\}=\left\{\frac{n^2-1}{n+8}\right\}$ .

  $\begin{array}{c}\left\{s_1\right\}=\left\{\frac{1^2-1}{1+8}\right\}\\ =\left\{\frac{1-1}{1+8}\right\}=0\\ \left\{s_2\right\}=\left\{\frac{2^2-1}{2+8}\right\}\\ =\left\{\frac{4-1}{2+8}\right\}=\frac{3}{10}\end{array}$

  $\begin{array}{c}\left\{s_3\right\}=\left\{\frac{3^2-1}{3+8}\right\}\\ =\left\{\frac{9-1}{3+8}\right\}=\frac{8}{11}\end{array}$

  $\begin{array}{c}\left\{s_4\right\}=\left\{\frac{4^2-1}{4+8}\right\}\\ =\left\{\frac{16-1}{4+8}\right\}=\frac{15}{12}=\frac{5}{4}\end{array}$

  $\begin{array}{c}\left\{s_5\right\}=\left\{\frac{5^2-1}{5+8}\right\}\\ =\left\{\frac{25-1}{5+8}\right\}=\frac{24}{13}\end{array}$

Therefore, the first five terms of the sequence are $0,\frac{3}{10},\frac{8}{11},\frac{5}{4}$ and $\frac{24}{13}$ .