Question

please solve it and find the value of n​

Answer 1

$\sf \Large Solution!!$

$\sf \to \dfrac{5^{n+3}-16\times 5^{n+1}}{12\times 5^{n}-2\times 5^{n+1}}$

$\sf Taking\:5^{n}\:as\:common.$

$\sf \to \dfrac{5^{n}(5^{3}-16\times 5)}{5^{n}(12-2\times 5)}$

Cancellation.

$\sf \to \dfrac{\cancel{5^{n}}(5^{3}-16\times 5)}{\cancel{5^{n}}(12-2\times 5)}$

$\sf \to \dfrac{125-80}{12-10}$

$\sf \to \dfrac{45}{2}$

$\sf \to 22\dfrac{1}{2}\:or\:22.5$