Question

25 to the power of (n-1) + 100 = 5 to the power of (2n-1)

Answer 1

Answer:

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Ans.

$\sf \: {25}^{n - 1} + 100 = {5}^{2n - 1}$

$\sf \: \implies {5}^{2n - 1} - {25}^{n - 1} = 100$

$\sf \: \implies {5}^{2n - 1} - {5}^{2n - 2} = 100$

$\sf \: \implies {5}^{2n } {5}^{ - 1} - {5}^{2n } {5}^{ - 2} = 100$

$\sf \: \implies {5}^{2n } ({5}^{ - 1} - {5}^{ - 2} ) = 100$

$\sf \: \implies {5}^{2n } ( \frac{1}{5} - \frac{1}{25} ) = 100$

$\sf \: \implies {5}^{2n } ( \frac{24}{25} ) = 100$

$\sf \: \implies {5}^{2n } = 100 \times \frac{25}{24}$

$\sf \: \implies {5}^{2n } = \frac{625}{6}$