Arithmetic and Geometric Sequences - General Forms of a Sequence

Arithmetic and Geometric Sequence

Sequence - an ordered list of terms or elements






Arithmetic sequence formula: In an Arithmetic Sequence, the difference between one term and the next is a constant. AKA the Common Difference.
ARITHMETIC FORMULA:
an =a1 +(n-1)d:
n: term number
a(n): nth term
a: first term
r: common difference

Geometric Sequence Formula: In a Geometric Sequence, each term is found by multiplying the previous term by a constant. AKA Common Ratio.
GEOMETRIC FORMULA:
an=a1 + r (n - 1):
n: term number
a(n): nth term
a: first term
r: common ratio

Example:        2, 4, 8, 16, 32, 64...

This sequence has a factor of 2 between each number. Each term ( except the first term ) is found by multiplying the previous term by 2.

Finite sequence - Function with domain 1, 2, 3.

Infinite sequence - Function with domain 1, 2, 3, 4....

Series - Sum of a sequence

Explicit formula - Each domain is an answer not based on any values.

Recursive formula - Each domain is an answer based on a previous answer