Question

What is the sum of a geometric series Sn=a+ar+ar2+ar3+…+arn-2+arn-1?

Answer 1

`Sn= (a(1-r^n))/(1-r)`

Explanation:

A geometric sequence is a sequence such that any element after the first is obtained by multiplying the preceding element by a constant called the common ratio which is denoted by r. The common ratio (r) is obtained by dividing any term by the preceding term.

from the given expression

the given data are

first term a1=
`a`

second term a2=
`ar`

third term a3=
`ar^2`

the common ratio is expressed as
`r=(a2)/(a1)`=
`(ar)/(a) = r`

Sum of Terms in a Geometric Progression

Finding the sum of terms in a geometric progression is easily obtained by applying the formulas:

`Sn= (a1(1-r^n))/(1-r)`

nth partial sum of a geometric sequence substituting the values of a1=a and the common ratio= r we have

`Sn= (a(1-r^n))/(1-r)`