Question

40 + 20 + 10 + … ; n = 10 Find the sum of each finite geometric series.

Answer 1

I've attached a picture below of the formula for a finite geometric sequence. It includes an infinite geometric sequence formula for your reference, too.


`a_1 = 40`

`r(ratio)= (1)/(2)`

`n=10`

Plug in the values.


`S_(10)=40*( (1- (1)/(2)^(10) )/(1- (1)/(2) ) )`

`S_(10)=40*( (1- (1)/(1024) )/((1)/(2) ))`

`S_(10)=40*( ((1023)/(1024) )/((1)/(2) ))`

`S_(10)=40*1.998046875`

`S_(10) = 79.921875`
S₁₀ ≈ 79.92