Question

1. What is the 15th partial sum of the geometric sequence (262,144; 32,768; 4,096; 512; ...)? Round to the nearest whole number, if needed.

Answer 1

`S_(15) = 299593`

Explanation:

Given

`262144,\ 32768,\ 4096,\ 512; ...`

Required

Determine the 15th partial sum

The nth partial sum of a geometric series is:

`S_n = a* (1 - r^n)/(1 - r)`

In this case:

`a = 262144`

`n = 15`

r is calculated as:

`r = (32768)/(262144)`

`r = 0.125`

Substitute values for a, r and n in
`S_n = a* (1 - r^n)/(1 - r)`

`S_(15) = 262144* (1 - 0.125^(15))/(1 - 0.125)`

`S_(15) = 262144* (1)/(0.875)`

`S_(15) = (262144* 1)/(0.875)`

`S_(15) = (262144)/(0.875)`

`S_(15) = 299593.142857`

`S_(15) = 299593` -- approximated