Geometric Sequences

The geometric sequence consists of numbers that have a common ratio.

An example is {4,8,16,32,64...} Each number is multiplied by two to achieve the next number.

The formula for a geometric series is:

a x r^n-1, where,

a= first term

r= common ratio n= term number

Find the 8th number in the sequence when the first number is 5 and the common ratio is 3.

U= 5 x (3)^(8-1)

Compound Interest = Principal amount ( 1 + Rate/100)^ Time Period

How much money is in an account after 3 years when 300 dollars is invested that is compounded annually and makes 5 percent interest?

I= 300 (1+5/100)^ 3

A Geometric Series serves the same purpose as a arithmetic sequence; to find the sum of a series.

The formula for a geometric series is:

S= a (r^n -1)/(r-1)

Example: Find the sum of the first 8 terms of a geometric sequence when the first number of the sequence is 5 and the common ratie is 2.

S= 5(2^8-1)/(2-1)