Question

The value of $\frac{5\times {\left(25\right)}^{n+1}+25\times {\left(5\right)}^{2n-1}}{25\times {\left(5\right)}^{2n}-105{\left(25\right)}^{n-1}}$ is

• A. 0
• B. 1
• C. $6\frac{1}{4}$
• D. $5\frac{1}{4}$

Answer 1

The correct option is C $6\frac{1}{4}$

$\frac{5\times {\left(25\right)}^{n+1}+25\times {\left(5\right)}^{2n-1}}{25\times {\left(5\right)}^{2n}-105{\left(25\right)}^{n-1}}$ $=\frac{5\times (5^2{)}^{n+1}+5^2\times 5^{2n-1}}{5^2\times 5^{2n}-21\times 5\times (5^2{)}^{n-1}}$

$=\frac{5^{2n+3}+5^{2n+1}}{5^{2n+2}-21\times 5^{2n-1}}$

$=\frac{5^{2n+1}(5^2+1)}{5^{2n-1}(5^3-21)}$

$=\frac{5^{(2n+1)-(2n-1)}\times 26}{(125-21)}$

$=\frac{5^2\times 26}{104}$

$=\frac{25}{4}=6\frac{1}{4}$