Mathematics, 23.01.2020 00:31 wizz2966
Given the sequence in the table below, determine the sigma notation of the sum for term 4 through term 15.
n an
1 4
2 −12
3 36
Answers: 1
![\bf \begin{array}{|cc|ll} \cline{1-2} n&a_n\\ \cline{1-2} 1&4\\ &\\ 2&\stackrel{4(-3)}{-12}\\ &\\ 3&\stackrel{-12(-3)}{36}\\ \cline{1-2} \end{array}\qquad \impliedby \textit{common ratio of "r" is -3} \\\\[-0.35em] ~\dotfill](/tpl/images/0466/5404/da4fb.png)
![\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}\\[-0.5em] \hrulefill\\ r=-3\\ a_1=4\\ n=15 \end{cases} \\\\\\ S_{15}\implies \displaystyle\sum\limits_{i=4}^{15}~4(-3)^{i-1}](/tpl/images/0466/5404/093dd.png)
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= nth term
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