Prove by induction $3+3 \cdot 5+ \cdots +3 \cdot 5^n = \frac{3(5^{n+1} -1)}{4}$ My question is:
Prove by induction that $$3+3 \cdot 5+ 3 \cdot 5^2+ \cdots +3 \cdot 5^n = \frac{3(5^{n+1} -1)}{4}$$ whenever $n$ is a nonnegative integer. 
I'm stuck at the basis step. 
If I started with $1$. I get the right hand side is $18$ which is clearly not even close. It says prove shouldn't it be always true?

For $n=1$, since $3 + 3 \times 5^1= 3+15 = 18$, there is no problem with the righthand side being $18$ too.
Note though that the base case is $n=0$, the condition being $n$ nonnegative, and then the lefthand side is $3$ as is the righthand side, which is $3 \times (5^{0+1}-1)/4 = 3$.
