Homework geometric series

A geometric series is a series or summation that sums the terms of a geometric sequence. There are methods and formulas we can use to find the value of a geometric series. It can be helpful for understanding geometric series to understand arithmetic series, and both concepts will be used in upper-level Calculus topics.

The geometric series sum is , where and a is the original value of the series. If , the series converges because the terms come increasingly close to zero; if or , the series diverges because the terms either increase in magnitude or remain equal.

Given the formula for geometric sequence, determine the first two terms, and then the 5th term. Also state the common ratio. 3. Given the geometric sequence, determine the formula, Then determine the 6th term. 1/3, 2/8, 4/17, 8/81, ... If playback doesn't begin shortly, try restarting your device.

Sequences whose rule is the multiplication of a constant are called geometric sequences, similar to arithmetic sequences that follow a rule of addition. Homework problems on geometric sequences often ask us to find the nth term of a sequence using a formula. Geometric sequences are important to understanding geometric series.