Question

5*(25)ⁿ⁺¹-25*(5)²ⁿ

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5*(5)^{​​​​2n+3}-(25)ⁿ⁺¹

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Answer 1

[5 * 5^(n+1) * 5^(n+1) - 5 * 5 * 5^2n] / [ 5 * 5^(2n+3) - 5^(n+1) * 5^(n+1)]
= [5^(2n+3) - 5^(2n+2)] / [5^(2n+4) - 5^(2n+2)]
Taking 5^(2n+2) common from both denominator and numerator
= (5-1)/5²-1
= 4/24
= 1/6