Chapter 9.1, Problem 33E

To determine

To match the given sequence $a_n=\frac{8}{\left(n+1\right)}$ with given graph of its first $10$ terms

  

Answer to Problem 33E

The given sequence match with graph $B$ .

Explanation of Solution

Given information :

Given sequence $a_n=\frac{8}{\left(n+1\right)}$

As we have $a_n=\frac{8}{\left(n+1\right)}$

For $n=1,a_1=\frac{8}{\left(1+1\right)}\Rightarrow a_1=\frac{8}{2}=4$

For $n=2,a_2=\frac{8}{\left(2+1\right)}\Rightarrow a_2=\frac{8}{3}$

For $n=3,a_3=\frac{8}{\left(3+1\right)}\Rightarrow a_3=\frac{8}{4}=2$

For $n=4,a_4=\frac{8}{\left(4+1\right)}\Rightarrow a_4=\frac{8}{5}$

Thus, the order pairs correspond to the given sequence $\left(1,4\right),\left(2,\frac{8}{3}\right),\left(3,2\right),\left(4,\frac{8}{5}\right)\mathrm{.......}$

Therefore, the graph with those order pairs is graph $C$ .

Hence, the given sequence match with graph $B$ .