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=[tex] \frac{a1(1-r^{n})}{1-r} [/tex]
in this case
Sn=[tex] \frac{1(1-5^{n})}{1-5} [/tex] or
Sn=[tex] \frac{1-5^{n}}{-4} [/tex]
so in this case
up to 5th term
S5=[tex] \frac{1-5^{5}}{-4} [/tex]
S5=[tex] \frac{1-3125}{-4} [/tex]
S5=[tex] \frac{-3124}{-4} [/tex]
S5=781
anyway
[tex] a_{n}=(5)^{n-1} [/tex] is the nth term
and
Sn=[tex] \frac{1-5^{n}}{-4} [/tex] is the summation up to the nth term
