Question

In Problems 29–36, the given pattern continues. Write down the nth term of a sequence $\left\{a_n\right\}$suggested by the pattern.

role="math" localid="1646738144824" $\frac{1}{2},\frac{2}{3},\frac{3}{4},\frac{4}{5},...$

Short answer

The nth term of the sequence is$a_n=\frac{n}{n+1}$

Step-by-step solution

Step 1. Write the given information

The given sequence is$\frac{1}{2},\frac{2}{3},\frac{3}{4},\frac{4}{5},...$

Step 2. Determine the pattern of the sequence and write down the nth term.

$a_1=\frac{1}{2},a_2=\frac{2}{3},a_3=\frac{3}{4}$

The pattern of the sequence is:

$$\begin{gathered} a_1=\frac{1}{2}=\frac{1}{1+1} \\ {a}_2=\frac{2}{3}=\frac{2}{2+1} \\ {a}_3=\frac{3}{4}=\frac{3}{3+1} \\ {a}_n=\frac{n}{n+1} \end{gathered}$$