Question

what is the sum of the first 5 terms if of a geometric series with a1=20 and r=1/4 the answer has to be an improper fraction

Answer 1

the sum of the term in a geometric sequence
Sn=
`(a1(1-r^n))/(1-r)`
where
there are n terms
r is common ratio
a1 is first term

Sn=
`(20(1-(1/4)^5))/(1-(1/4))`
Sn=
`(20(1-(1/1024)))/(3/4)`
Sn=
`(20(1023/1024))/(3/4)`
Sn=
`(1705)/(64)`