Question

\frac { 6 ^ { n + 2 } - 6 ^ { n } } { 6 ^ { n + 1 } + 6 ^ { n } }

Answer 1

Answer:  5

Work Shown:

$m = \frac{6^{n+2}-6^{n}}{6^{n+1}+6^{n}}\\\\m = \frac{6^{n}*6^2-6^{n}}{6^{n}*6^1+6^{n}}\\\\m = \frac{6^{n}*36-6^{n}}{6^{n}*6+6^{n}}\\\\m = \frac{6^{n}(36-1)}{6^{n}(6+1)}\\\\m = \frac{6^{n}(35)}{6^{n}(7)}\\\\m = \frac{35}{7}\\\\m = 5$

Therefore,

$\frac{6^{n+2}-6^{n}}{6^{n+1}+6^{n}}=5$