Solve the equation {5}^(n + 1) - {5}^(n) + {5}^(n - 1) = 105 ​

Question

Solve the equation

`{5}^(n + 1) - {5}^(n) + {5}^(n - 1) = 105`
​

Answer 1

n=2 is the correct answer yes

Answer 2

n=2

Explanation:

Hello, please consider the following.

`{5}^(n + 1) - {5}^(n) + {5}^(n - 1) = 105\\\\5^(n-1)(5^2-5+1)=5^(n-1)(25-5+1)=21*5^(n-1)=105\\\\5^(n-1)=(105)/(21)=5=5^1\\\\\text{It means that}\\\\n-1=1 <=> n=2`

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Thank you