# How do you write the first five terms of the sequence a_n=n/(n+2)?

Nov 30, 2017

The first 5 terms are: $\left\{\frac{1}{3} , \frac{2}{4} , \frac{3}{5} , \frac{4}{6} , \frac{5}{7}\right\}$. (I didn't reduce so the pattern would be more clear.)

#### Explanation:

I'm assuming that we start at $n = 1$ for this.

Substitute $n = 1$ to get ${a}_{1} = \frac{1}{3}$.
Substitute $n = 2$ to get ${a}_{2} = \frac{2}{4} = \frac{1}{2}$.
Substitute $n = 3$ to get ${a}_{3} = \frac{3}{5}$.
Substitute $n = 4$ to get ${a}_{4} = \frac{4}{6} = \frac{2}{3}$.
Substitute $n = 5$ to get ${a}_{5} = \frac{5}{7}$.

So the first 5 terms are: $\left\{\frac{1}{3} , \frac{2}{4} , \frac{3}{5} , \frac{4}{6} , \frac{5}{7}\right\}$.