Answer
$a_{1}$ = $\frac{6}{5}$
$a_{2}$ = $ \frac{5}{4}$
$a_{3}$ = $ \frac{4}{3} $
$a_{4}$ = $\frac{3}{2}$
$a_{5}$ = $=2$
Work Step by Step
Sequence: $a_{n}=\frac{n-7}{n-6}$
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.
$a_{1}$ = $\frac{1-7}{1-6}= \frac{-6}{-5} = \frac{6}{5}$
$a_{2}$ = $\frac{2-7}{2-6}= \frac{-5}{-4} =\frac{5}{4}$
$a_{3}$ = $\frac{3-7}{3-6}= \frac{-4}{-3}= \frac{4}{3} $
$a_{4}$ = $\frac{4-7}{4-6}= \frac{-3}{-2} =\frac{3}{2}$
$a_{5}$ = $\frac{5-7}{5-6}= \frac{-2}{-1}=2$
The first five terms of the sequence are $\frac{6}{5}, \frac{5}{4}, \frac{4}{3}, \frac{3}{2},$ and 2.
