Question

Find S5 for a geometric series for which a1=81 and r=1/9.

Answer 1

`S_5=91(10)/(81)`

Step-by-step explanation

The sum of the first
`n` terms of a geometric sequence is given by;

`S_n=(a_1(1-r^n))/(1-r) ,-1<\:r<\:1`

Where
`n`, is the number of terms and
`a_1` is the first term.

When
`n=5`, we have
`a_1=81`, we get;

`S_5=(81(1-((1)/(9))^5))/(1-(1)/(9))`

`S_5=(81(1-(1)/(59049)))/(1-(1)/(9))`

`S_5=(81((59048)/(59049)))/((8)/(9))`

`S_5=(7381)/(81)`

`S_5=91(10)/(81)`