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Leno4ka [110]
3 years ago
11

What is the sum of the first eight terms of a geometric series whose first term is 3 and whose common ratio is .5 ?

Mathematics
2 answers:
ser-zykov [4K]3 years ago
7 0
\bf \qquad \textit{sum of a finite geometric sequence}
\\ \quad \\
 S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad 
\begin{cases}
n=\textit{last term}\\
a_1=\textit{first term}\\
r=\textit{common ratio}
\end{cases}
\\ \quad \\
S_8=3\left( \cfrac{1-0.5^8}{1-0.5} \right)
stellarik [79]3 years ago
6 0

Answer:  The required sum of first eight terms of the given geometric series is 5.98.

Step-by-step explanation:  We are given to find the sum of first eight terms of a geometric series whose first term is 3 and whose common ratio is 0.5.

We know that

the sum of first n terms of a geometric series with first term a and common ratio r is given by

S_n=\dfrac{a(1-r^n)}{1-}.

For the given geometric series, we have

first term, a = 3  and  common ratio, r = 0.5.

So, the sum of first eight terms of the given geometric series will be

S_8\\\\\\=\dfrac{a(1-r^8)}{1-r}\\\\\\=\dfrac{3\left(1-\left(\frac{1}{2}\right)^8\right)}{1-\frac{1}{2}}\\\\\\=\dfrac{3\left(1-\frac{1}{256}\right)}{\frac{1}{2}}\\\\\\=3\times2\times\dfrac{256-1}{256}\\\\\\=3\times\dfrac{255}{128}\\\\\\=\dfrac{765}{128}\\\\=5.98.

Thus, the required sum of first eight terms of the given geometric series is 5.98.

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============================

Work Shown:

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--------

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--------

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