Answer
$a_{1}$ = $\frac{6}{5}$
$a_{2}$ = $\frac{7}{6}$
$a_{3}$ =$ \frac{8}{7}$
$a_{4}$ = $\frac{9}{8}$
$a_{5}$ = $ \frac{10}{9}$
Work Step by Step
Sequence: $a_{n}=\frac{n+5}{n+4}$
To find the nth term of a sequence we substitute n into the sequence and evaluate it. To find the first 5 terms, we substitute 1, 2, 3, 4, and 5 and evaluate.
$a_{1}$ = $\frac{1+5}{1+4}= \frac{6}{5}$
$a_{2}$ = $\frac{2+5}{2+4}= \frac{7}{6}$
$a_{3}$ = $\frac{3+5}{3+4}= \frac{8}{7}$
$a_{4}$ = $\frac{4+5}{4+4}= \frac{9}{8}$
$a_{5}$ = $\frac{5+5}{5+4}= \frac{10}{9}$
The first five terms of the sequence are $\frac{6}{5}, \frac{7}{6}, \frac{8}{7}, \frac{9}{8}, \text{ and } \frac{10}{9}.$
