9.1 Sequences And Series

Sequence- an ordered list of numbers

ex. 8, 13, 18, 23, 28, 33, . . .

(each number here is increased by 5)

Recursive Formula (for above example)

(you must labelwereevery sequence begins)

(above ex. labeled recursively)

next term=known term +5

Explicit Formula (for above example)

*only for above sequence*

Important Notes

• each sequence has its own recursive and explicitformulas
• explicit formulas can look like anything whereas recursive formulas follow the above format
• use theexplicit formula of a sequence to find the nth term of the sequence

EX. a1=1

a2=2

a3=4

a4=8

EX. -1/2, 4/4, -9/8, 16/16, -25/32, 36/64

Factorials

A factorial is a positive integer n, denoted by n!, that is the product of all positive integers less than or equal to n

ex. 5!= (1)(2)(3)(4)(5)

Solving Factorials

ex.

(you can reduce this by canceling out like terms and reducing others)

ex.

(cancel all like terms out now)