Question

Which expression represents the series 1+5+25+125+625

Answer 1

First, see that this is a partial sum of a geometric series. This is because each term is multiplied by 5 to get the next term. Knowing that common ratio of 5, you will also need to know the number of terms, and the first term.
Plug into this equation: An = A1(r)^n-1

Answer 2

So if you want to find the nth term so
1st term=1
2nd term=5
3rd term=25
we notice that 5^1=5 and 5^2=25 , but they are on the second ones so
the expression is

the nth term=5^(n-1)
so 1st term=5^(1-1)=5^0=1
2nd term=5^(2-1)=5^1=5
3rd term=5^(3-1)=5^2=25
and so on


the expression is 5^(n-1)