The geometric series' first seven terms are added together to form a sum equal to \(\boldsymbol{16383}\).
Geometric Series
A geometric series is the summation of an unlimited number of terms with a fixed ratio between them.
Let \(\boldsymbol{a,r}\) denote the first term and the common ratio between the consecutive terms respectively.
Consider the geometric series: \(3+12+48+192+...\)
\(\boldsymbol{a=3}\)
\(r=\frac{12}{3}\)
\(= \boldsymbol{4}\)
\(\boldsymbol{S_n=\frac{a(1-r^n)}{1-r} }\)
\(S_n =\frac{3(1-4^7)}{1-4}\)
\(=\frac{3(16383)}{3}\)
\(=16383\)
So, the geometric series' first seven terms are added together to form a sum equal to \(\boldsymbol{16383}\).
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