Predicting What Comes Next : Exploring Sequences and Progressions

A sequence is an ordered list

A sequence is an ordered list of numbers where each number is a term of the sequence. Sequences may be finite or infinite.

A finite sequence has a limited

A finite sequence has a limited number of terms, while an infinite sequence continues without end. The sequence 6, 12, 24, 48, 96 is finite.

An explicit formula uses the term

An explicit formula uses the term position number n to calculate the term directly. For odd numbers, the explicit rule is u_n = 2n - 1.

A recursive rule gives a term

A recursive rule gives a term using earlier term(s). For an AP, the rule is t_1 = a, t_n = t_{n-1} + d for n ≥ 2. The Virahānka–Fibonacci sequence is

The odd number sequence is 1

The odd number sequence is 1, 3, 5, 7, 9, 11, ... and each consecutive pair differs by 2. Its nth term is u_n = 2n - 1.