What Is The Formula For The General Term Of A Geometric Sequence Complete Guide

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what is the formula for the general term of a geometric sequence. The nth term from the end of the GP with the last term l and common ratio r l rn 1. The general formula to find the nth term is.

Determine The Number Of Terms Type 2 Geometric Series Sequence And Series Geometric Sequences
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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.