Question

4^n+2-4^n+1/5*4^n-4^n

Answer 1

Answer :

Now,

$\frac{ {4}^{n + 2} - {4}^{n + 1} }{5 \times {4}^{n} - {4}^{n} } \\ \\ = \frac{ {4}^{n} ( {4}^{2} - {4}^{1} )}{ {4}^{n} (5 - 1)} \\ \\ = \frac{16 - 4}{4} \\ \\ = \frac{12}{4} \\ \\ = \bold3$

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Answer 2

Hello!

$\dfrac{\sf 4^{n+2} - 4^{n+1}}{\sf 5\: x\: 4^{n} - 4^{n}}$

= $\dfrac{\sf \cancel{4^{n}}(4^{2} - 4^{1})}{\sf \cancel{4^{n}}(5 - 1)}$

= $\dfrac{\sf 16 - 4}{\sf 4}$

= $\dfrac{\sf 12}{\sf 4} = \sf 3$

∴ $\boxed{\dfrac{\sf 4^{n+2} - 4^{n+1}}{\sf 5 \:x \:4^{n} - 4^{n}} = \sf 3}$

Cheers!