Question

\[\frac{5^{n + 2} - 6 \times 5^{n + 1}}{13 \times 5^n - 2 \times 5^{n + 1}}\]  is equal to

Options

• \[\frac{5}{3}\]

• \[- \frac{5}{3}\]

• \[\frac{3}{5}\]

• \[- \frac{3}{5}\]

Answer 1

We have to simplify `(5^(n+2) - 6xx 5^(n+1))/(13 xx 5^n - 2 xx5^(n+1))`

Taking `5^2` as a common factor we get

`(5^(n+2) - 6xx 5^(n+1))/(13 xx 5^n - 2 xx5^(n+1)) = (5^n(5^2 -6 xx 5^1))/(5^n(13-2 xx 5^1))`

                                      `= (5^n(25-30))/(5^n(13-10))`

                                      ` = (-5)/3`