Mathematics, 13.07.2019 19:30 lol1516
Find the sum of a finite geometric series. the smiths spent $2,000 on clothes in a particular year. if they increase the amount they spend on clothes by 10% each year, the smiths will spend a total of $ on clothing in 4 years.
Answers: 1
.![\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=2000\\r=1.1\\n=4\end{cases}\\\\\\S_4=2000\left[ \cfrac{1-(1.1)^4}{1-1.1} \right]\implies S_4=2000\left(\cfrac{-0.4641}{-0.1} \right)\\\\\\S_4=2000(4.641)\implies S_4=9282](/tpl/images/0085/9001/8d214.png)
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Find the sum of a finite geometric series. the smiths spent $2,000 on clothes in a particular year....
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