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Marrrta [24]
3 years ago
9

What is the sum of the infinite geometric series represented by (picture)

Mathematics
1 answer:
SSSSS [86.1K]3 years ago
8 0
ANSWER

D.
720


EXPLANATION

The infinite geometric series given to us is,

\sum_{n=1}^{\infty}180\times (\frac{3}{4})^{n-1}


The first term of this series is,



a_1=180\times (\frac{3}{4})^{1-1}

This implies that,

a_1=180\times (\frac{3}{4})^{0}


a_1=180


a_2=180\times (\frac{3}{4})^{2-1}


a_2=180\times (\frac{3}{4})^{1}



a_2=135



The common ratio of this sequence,



r =  \frac{a_2}{a_1}


r =  \frac{135}{180}


r =  \frac{3}{4}


The sum to infinity of this series is given by the formula,

S_{\infty}=\frac{a_1}{1 -  r}


We substitute the above values to get,

S_{\infty}=\frac{180}{1 -   \frac{3}{4} }


This simplifies to

S_{\infty}=\frac{180}{ \frac{1}{4} }

This implies that,

S_{\infty}=180 \times 4


S_{\infty}=720

The correct answer is D.
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