$\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ S_n=\displaystyle\sum \limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio} \end{cases} \\\\[-0.35em] ~\dotfill$

$\bf S_{20}=\displaystyle\sum \limits_{n=1}^{\stackrel{\stackrel{n}{\downarrow }}{20}}~\stackrel{\stackrel{a_1}{\downarrow }}{3}(\stackrel{\stackrel{r}{\downarrow }}{1.5})^{n-1}\implies S_{20}=3\left(\cfrac{1-1.5^{20}}{1-1.5} \right)\implies S_{20}=3\left(\cfrac{1-\stackrel{\approx}{3325.3}}{-0.5} \right) \\\\\\ S_{20}=3\left(\cfrac{-3324.3}{-0.5} \right)\implies S_{20}=3(6648.6)\implies S_{20}=19945.8$

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3 years ago

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Victor needs to calculate the number of miles per gallon his car averages. His car's gas tanks holds 15 gallons of gas. Write an

krek1111 [17]

Since you're looking for the unit rate, you can start do this:
$mpg= \frac{miles}{gallon}\\
y=\frac{x}{15}$
And yes, $15y=x$ is also correct, it's just switching around the 15

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3 years ago

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How do the areas of the parallelogram compare?

IrinaK [193]

The first choice is right, area of 1 is 20, area of 2 is 16

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3 years ago

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