Question

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

Answer 1

1(5)^0 + 1(5)^1 + 1(5)^2...

The expression representing the series would be

f(x) = 5^(x-1)

Answer 2

It is a geometric sequence
an=a1(r)^(n-1)
a1=first term
r=common ratio
n=which term
first term is 1
common ratio is 5
an=1(5)^(n-1)

that is the equatin/formulf for the nth term

if you want a summation formula of the sequence to the nth term
Sn=$\frac{a1(1-r^{n})}{1-r}$
in this case
Sn=$\frac{1(1-5^{n})}{1-5}$ or
Sn=$\frac{1-5^{n}}{-4}$
so in this case
up to 5th term

S5=$\frac{1-5^{5}}{-4}$
S5=$\frac{1-3125}{-4}$
S5=$\frac{-3124}{-4}$
S5=781


anyway
$a_{n}=(5)^{n-1}$ is the nth term
and
Sn=$\frac{1-5^{n}}{-4}$ is the summation up to the nth term