Mathematics, 25.06.2019 15:00 natalie2sheffield
What is the sum of an infinite geometric series if a1 = 144 and r = 1⁄4? a. 192 b. 288 c. 576 d. 252
Answers: 1
![\bf \qquad \qquad \textit{sum of a infinite geometric sequence} \\\\ S=\sum\limits_{i=0}^{\infty}\ a_1\cdot r^{i}\implies S=\cfrac{a_1}{1-r}~~ \begin{cases} a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ \qquad 0\leqslant |r| \leqslant 1\\[-0.5em] \hrulefill\\ r=\frac{1}{4}\\ a_1=144 \end{cases} \\\\\\ S=\cfrac{144}{1-\frac{1}{4}}\implies S=\cfrac{144}{\frac{3}{4}}\implies S=192](/tpl/images/0016/0664/a0d33.png)
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What is the sum of an infinite geometric series if a1 = 144 and r = 1⁄4? a. 192 b. 288 c. 576 d. 25...
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