Sequence:  A sequence is nothing more than a list of numbers written in a specific order. 

Arithmetic Sequence: An arithmetic sequence goes from one term to the next by always adding (or subtracting) the same value.

Geometric Sequence: A geometric sequence goes from one term to the next by always multiplying (or dividing) by the same value. 

Series:  the sum of the terms of a sequence.

Equations: Arithmetic equations...

an=a1=(n-1)d (to find the nth term of the sequence use this equation) and Sn=n/2(a1+an) (sum equation)

Geometric equations...

an=a1xr^n-1 (to find the next term in the sequence use this equation) and Sn=a1(1-r^n)/1-r (sum equation)

Sequences and Series

Sequences and Series Practice Problems

2, 4, 6, 8, 10... is an arithmetic sequence with the common difference 2.

Find the 6th term:

a6= 2+(6-1)2

2+10=12

a6=12

Now find the sum of the first 5 terms:

Sn=5/2(2+10)

5/2(12)=30

Sn=30

Sequences and Series Practice Problems

5, 10, 20, 40, 80... is a geometric sequence with each number being multiplied by 2.

Find the 6th term:

a6= 5x2^6-1

5x32= 160

Find the sum of first 5 terms:

S5=5(1-2^5)/1-2

-155/-1= 155

s5=155

Permutations and Combinations

Permutation:

A collection of things, where the order is important.

"The combination to the safe is 472"

Equation:

Combination:

A collection of things, in which the order does not matter.

"My fruit salad is a combination of apples, grapes and bananas" 

Equation:

Permutation Example

How many unique ways are there to arrange the letters in the word DEN?

3x2x1= 6