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Question
\[\frac{5^{n + 2} - 6 \times 5^{n + 1}}{13 \times 5^n - 2 \times 5^{n + 1}}\] is equal to
Options
\[\frac{5}{3}\]
\[- \frac{5}{3}\]
\[\frac{3}{5}\]
\[- \frac{3}{5}\]
Solution
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`
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