Saturday, 13 April 2019

How to find the sum of a geometric sequence with an upper bound of n

Let's say I have an equation that includes the Sum, $\sum_{i=0}^n \frac12 (-5)^i$ where $n$ is the last term in the sequence.



We know that this sequence is geometric because the common difference is a multiple of $-5$ meaning that every term is multiplied by $-5$.



The sequence goes like:
$$\frac12, \frac{-5}{2}, \frac{25}2, \frac{-125}2, \ldots, n$$




My question is, how do we find the sum of this geometric sequence when the upper bound of the sigma notation is $n$? Is there some sort of formula that we can use in order to find the sum?



Thanks in advance!

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