Question

Solve the equation 0%20%7B5%7D%5E%7Bn%20-%201%7D%20%20%3D%20105" id="TexFormula1" title=" {5}^{n + 1} - {5}^{n} + {5}^{n - 1} = 105" alt=" {5}^{n + 1} - {5}^{n} + {5}^{n - 1} = 105" align="absmiddle" class="latex-formula">
​

Answer 1

N=2 is the correct answer yes

Answer 2

Answer:

n=2

Step-by-step explanation:

Hello, please consider the following.

${5}^{n + 1} - {5}^{n} + {5}^{n - 1} = 105\\\\5^{n-1}(5^2-5+1)=5^{n-1}(25-5+1)=21*5^{n-1}=105\\\\5^{n-1}=\dfrac{105}{21}=5=5^1\\\\\text{It means that}\\\\n-1=1 n=2$

Let me know if you need more details.

Thank you