sequences

Recursive formula of arithmetic sequences

an = an-1 + d. d is the common difference

Sequence

A number pattern that follows a predictable rule.

Term

Each number in the sequence

Arithmetic sequence

When the difference between each term is always equal

Common difference

The difference between the terms in the sequence

Explicit formula for arithmetic sequences

an=a1 + (n-1)d, where a1 is the first term, n is the term number being found, and d is the common difference

Geometric sequence

When you multiply the same number to get the next term

common ratio

Difference between consecutive terms in geometric sequences

Recursive formula for geometric sequences

an = an-1 ( r) where r is the common ratio

Explicit formula for geometric sequences

an=a1 (r^n-1) where r is the common ratio and n is the term number being found

Geometric sequences are basically

Exponential growth

Explicit formula (pyramidal)

P(n) = n(n+1)(2n +1)/6

Fibonacci sequence

Each term is the sum of the two terms before it

Over time, a geometric sequence will eventually ___ an arithmetic sequence

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