How do I evaluate the following?? I keep using a= 1/5 and r=1/4 for
$a\frac{1-r^n}{1-r}$but I obviously keep getting the wrong answer. I know how to calculate a geometric sum from an equation but it is difficult for me to calculate it from a set of numbers (
1 Answer
$\begingroup$Each term is $1/4$ the previous term, so $r=1/4$. Your first term, corresponding to the zero power of $1/4$ is $1/5$, so this is your a. Then, to figure out where the series terminates, you must find out what power of $1/4$ yields the equality $$ \frac{1}{5*4^n}=\frac{1}{20,480}\Rightarrow 4^n=\frac{20,480}{5}=2*2^{11}=2^{12}=4^6\Rightarrow n=6 $$ Then use the familiar formula for a finite geometric sum with n terms, $$ \sum_{k=1}^{n}ar^k=a\frac{1-r^{n+1}}{1-r} $$ with $r=1/4$ and $a=1/5$ as we found.
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