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Sveta_85 [38]
3 years ago
5

Find s10 for a geometric series with first term 10 and a common ratio 4

Mathematics
2 answers:
CaHeK987 [17]3 years ago
4 0
The sum of a geometric sequence where the first term is a1 and the common ratio is r and n is which term is
S_{n}=\frac{a_1(1-r^n)}{1-r}

so
given first term of 10 and common ratio 4 and n=10

S_{10}=\frac{10(1-4^{10})}{1-4}
S_{10}=\frac{10(1-1048576)}{-3}
S_{10}=\frac{10(-1048575)}{-3}
S_{10}=\frac{-10485750}{-3}
S_{10}=3495250
yulyashka [42]3 years ago
3 0
\bf \qquad \qquad \textit{sum of a finite geometric sequence}\\\\
S_n=\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}\\
----------\\
n=10\\
r=4\\
a_1=10
\end{cases}
\\\\\\
S_{10}=10\left( \cfrac{1-4^{10}}{1-4} \right)
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