Answered

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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.

Sagot :

MrRoyal

Answer:

[tex]S_{15} = 299593[/tex]

Step-by-step explanation:

Given

[tex]262144,\ 32768,\ 4096,\ 512; ...[/tex]

Required

Determine the 15th partial sum

The nth partial sum of a geometric series is:

[tex]S_n = a* \frac{1 - r^n}{1 - r}[/tex]

In this case:

[tex]a = 262144[/tex]

[tex]n = 15[/tex]

r is calculated as:

[tex]r = \frac{32768}{262144}[/tex]

[tex]r = 0.125[/tex]

Substitute values for a, r and n in [tex]S_n = a* \frac{1 - r^n}{1 - r}[/tex]

[tex]S_{15} = 262144* \frac{1 - 0.125^{15}}{1 - 0.125}[/tex]

[tex]S_{15} = 262144* \frac{1}{0.875}[/tex]

[tex]S_{15} = \frac{262144* 1}{0.875}[/tex]

[tex]S_{15} = \frac{262144}{0.875}[/tex]

[tex]S_{15} = 299593.142857[/tex]

[tex]S_{15} = 299593[/tex] -- approximated

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