Question

Write down the first five terms of the sequence.

$\left\{S_n\right\}=\left\{\frac{n^2-1}{n+8}\right\}$

Short answer

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

Step-by-step solution

Given information:

Consider , $\left\{S_n\right\}=\left\{\frac{n^2-1}{n+8}\right\}$

To find the values of$S_1,S_2,S_3,S_{4}and{S}_5.$

To find S1 :

Put $n=1$,

role="math" localid="1647414124167" $$\begin{gathered} S_1=\frac{1^2-1}{1+8} \\ =\frac{0}{9} \\ =0 \end{gathered}$$

To find S2 :

Put $n=2$,

$S_2=\frac{2^2-1}{2+8}$

$$\begin{gathered} =\frac{4-1}{10} \\ =\frac{3}{10} \end{gathered}$$

To find S3 :

Put $n=3$,

$$\begin{gathered} S_3=\frac{3^2-1}{3+8} \\ =\frac{9-1}{11} \\ =\frac{8}{11} \end{gathered}$$

To find S4 :

Put $n=4$,

$$\begin{gathered} S_4=\frac{4^2-1}{4+8} \\ =\frac{16-1}{12} \\ =\frac{15}{12} \\ =\frac{5}{4} \end{gathered}$$

To find S5 :

Put $n=5,$

$$\begin{gathered} S_5=\frac{5^2-1}{5+8} \\ =\frac{25-1}{13} \\ =\frac{24}{13} \end{gathered}$$