Displaystyle sum _k1nark-1ar0ar1ar2ar3cdots arn-1. A_n a_1 rn-1 There exists a formula that can add a finite geometric sequence. The general form of the sequence is a 1 a 1 r 2 a 1 r 3 a 1 r 4 a 1 r n 1We dont always want to write out the entire sequence all the time so instead of writing everything out 5 10 20 40 80 160 we can use a much shorter formula.
This example demonstrates how useful the general formula for determining an arithmetic series is especially when the series has a large number of terms.
A What is r for this series. Displaystyle sum _k1nark-1ar0ar1ar2ar3cdots arn-1. S_n frac a_1 1- rn1-r for r 1. B The variable x can take on any numerical value.