Evaluate $5+4\cdot 5+4\cdot5^2+4\cdot5^3+4\cdot5^4+4\cdot5^5$ 
Evaluate
  $$5+4\cdot 5+4\cdot5^2+4\cdot5^3+4\cdot5^4+4\cdot5^5.$$
  The options are $5^6$, $5^7$, $5^8$, $5^9$, $5^{10}$.

I'm new to this site. I came across this question in an Olympiad foundation site. I have no idea how to solve it. Can I get the answer of this question. Thanks.

$$a=5+4.5+4.5^2+4.5^3+4.5^4+4.5^5\to \times 5\\5a=25+4.5^2+4.5^3+4.5^4+4.5^5+4.5^6$$ now $5a-a= ?$
$$\quad{5a-a=(25-5)-(4.5)+(4.5^2-4.5^2)+(4.5^3-4.5^3)+(4.5^4-4.5^4)+(4.5^5-4.5^5)+4.5^6\\\to 5a-a=4.5^6 \\4a=4.5^6\\a=5^6}$$
