A prize was awarded to 40 women and 678 men

1 answer:

6 0

The fraction of winners that were women is 40/718 which simplifies to 20/359

The fraction of winners that were men is 678/718 which simplifies to 339/359

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Given the sequence in the table below, determine the sigma notation of the sum for term 4 through term 15.

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It's a geometric sequence.

$4,-12,36,... \\ \\
a_1=4 \\
r=\frac{a_2}{a_1}=\frac{-12}{4}=-3 \\ \\
a_n=a_1 \times r^{n-1} \\
a_n=4 \times (-3)^{n-1} \\
a_n=4 \times (-3)^{-1} \times (-3)^n \\
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It's the sum for term 4 through term 15.

$\boxed{ \sum\limits_{n=4}^{15} (\frac{4}{3}(-3)^n)}$

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