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sergij07 [2.7K]
3 years ago
12

What is the sum of the first 4 terms of a geometric sequence that has a first term of 2 and a ratio (multiplier) of 8?

Mathematics
1 answer:
taurus [48]3 years ago
6 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}\\ ----------\\ a_1=2\\ r=8\\ n=4 \end{cases} \\\\\\ S_4=2\left( \cfrac{1-8^4}{1-8} \right)\implies S_4=2\left( \cfrac{-4095}{-7} \right) \\\\\\ S_4=2(585)\implies S_4=1170

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