How does $3(5^{k+1} + 4 \cdot 5^{k+1} - 1) / 4$ lead to $3(5^{k+2} - 1) / 4$?

Question

I am struggling with following from an example, which I hope someone can explain for me.

How does the first expression lead to the second? $$3(5^{k+1} + 4 \cdot 5^{k+1} - 1) / 4 \quad\to\qquad3(5^{k+2} - 1) / 4$$

Answer 1

It's because $5^{k+1}+4\cdot5^{k+1}=(1+4)\cdot5^{k+1}=5\cdot5^{k+1}=5^{k+2}.$