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

Answer:

$S_{15} = 299593$

Step-by-step explanation:

Given

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

Required

Determine the 15th partial sum

The nth partial sum of a geometric series is:

$S_n = a* \frac{1 - r^n}{1 - r}$

In this case:

$a = 262144$

$n = 15$

r is calculated as:

$r = \frac{32768}{262144}$

$r = 0.125$

Substitute values for a, r and n in $S_n = a* \frac{1 - r^n}{1 - r}$

$S_{15} = 262144* \frac{1 - 0.125^{15}}{1 - 0.125}$

$S_{15} = 262144* \frac{1}{0.875}$

$S_{15} = \frac{262144* 1}{0.875}$

$S_{15} = \frac{262144}{0.875}$

$S_{15} = 299593.142857$

$S_{15} = 299593$ -- approximated