Sequences and Series

Infinite Geometric Series Formula

*Only if |r| < 1*

Find the Sum of the Geometric Series - 3 + 0.3 + 0.003 + ...

10/3

Recursive Arithmetic Sequence Example: First term: 5, Common difference: 2. Find 4th term

11

Find the n = 20 term in the following Arithmetic Sequence. 25, 50, 75, 100, 125, ...

500

What is the sum of the nth term? 2, 8, 32, 128, ... n=9

A(9)=131,072

Sum of an Infinite Geometric Sequence

Can only be done if the r value is less than one

Converging & Diverging Geometric Sequences

Diverging: Increasing Converging: Decreasing You can find the sum of an infinite geometric series if the r value is less than 1.

Geometric Sequence Definition

Is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

Determine whether the sequences is arithmetic, if so find the common difference. 2, 4, 8, 16, 32

Not arithmetic

Arithmetic Sequence

Numbers that

Geometric Series Definition

Sum of a geometric sequence

Find the recursive equation for this Geometric Sequence 0.2, -1, 5, -25, ...

a(n)=a(n-1)*(-5)

Arithmetic Recursive Equation

an = nth term, a1 = first term, d = common difference

Find the Sum of the Geometric Series - 4(.3) + 4(.3)^2 + 4(.3)^3 + ... + 4(.3)^12

~1.714