Mathwords logoReference LibraryMathwords

Geometric Sequence

Geometric Sequence
Geometric Progression

A sequence such as 2, 6, 18, 54, 162 or a1, 1/3, 1/9, 1/27, 1/81 — a geometric sequence with common ratio r = 1/3 which has a constant ratio between terms. The first term is a1, the common ratio is r, and the number of terms is n.

 

Explicit formula a_n = a_1 * r^(n-1) with two examples: (1) 2,6,18,54,162 where a_2=2, r=3, n=5; (2) 3,1,1/3,1/9,1/27,1/81...

 

 

See also

Geometric series, infinite geometric series, arithmetic sequence