Question

$\frac{5^{n+2}-6\times 5^{n+1}}{13\times 5^n-2\times 5^{n+1}}isequalto$

• A. $\frac{5}{3}$
• B. $-\frac{5}{3}$
• C. $\frac{3}{5}$
• D. $-\frac{3}{5}$

Answer 1

Given $\frac{5^{n+2}-6\times 5^{n+1}}{13\times 5^n-2\times 5^{n+1}}=\frac{5^n(5^2-6\times 5^1)}{5^n(13-2\times 5^1)}$ [Since, $a^{m+n}=a^m\times a^n$]
$=\frac{5^2-(6\times 5)}{13-(2\times 5)}=\frac{25-30}{13-10}=\frac{-5}{3}$