Question #7a5dd

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Question #7a5dd

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Answer 1 · 2017-09-14T15:30:31

63.9375

Explanation:

The formula of the geometric series (sum of n-terms of a pattern):
$S_{n} = \frac{a (1 - r^{n})}{1 - r}$ $S_n=(a(1-r^n))/(1-r)$
Where n is the number of terms, 10 in your case, and r is the common ratio.

The common ratio can be found by dividing any term from the term before:
$r = \frac{a_{n + 1}}{a_{n}}$ $r=a_(n+1)/a_n$

Let us take any two terms and divide them:
$\frac{a_{2}}{a_{1}} = \frac{16}{32} = \frac{1}{2}$ $a_2/a_1=16/32=1/2$

Now that we have the common ratio $(\frac{1}{2})$ $(1/2)$ and the first term (32), we can calculate the sum.
$S_{10} = \frac{32 (1 - {(\frac{1}{2})}^{10})}{1 - (\frac{1}{2})}$ $S_10=(32(1-(1/2)^10))/(1-(1/2))$

Simplifying:
$S_{10} = \frac{32 - \frac{32}{2^{10}}}{\frac{1}{2}}$ $S_10=(32-32/2^10)/(1/2)$

Putting this in the calculator:
$S_{10} = \frac{32 - \frac{32}{2^{10}}}{\frac{1}{2}} = 63.9375$ $S_10=(32-32/2^10)/(1/2)=63.9375$

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Question #7a5dd

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