Question

$\frac{5^{n+3}-6\times 5^{n+1}}{9\times 5^n-5^n\times 2^2}$ = 19

• A. True
• B. False

Answer 1

The correct option is A

True

Given: $\frac{5^{n+3}-6\times 5^{n+1}}{9\times 5^n-5^n\times 2^2}$

= $\frac{5^{n+1+2}-6\times 5^{n+1}}{9\times 5^n-5^n\times 2^2}$

= $\frac{(5^{n+1}\times 5^2)-6\times 5^{n+1}}{9\times 5^n-5^n\times 2^2}$ ($\because a^m\times a^n=a^{(m+n)}$)

Taking the common factor out we get

$\frac{5^{n+1}(5^2-6)}{5^n(9-2^2)}$

$\Rightarrow$ $\frac{5^{n+1}\left(19\right)}{5^n\left(5\right)}$

$\Rightarrow$ $\frac{5^{n+1}\left(19\right)}{5^{n+1}}$

$\Rightarrow$ 19