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a_1 - & the first term, q - the common ratio. Definition: A next term of an geometric sequence obtain by multiply the common ratio q to a previous term. a_{n+1} = a_n * q. Examples: a_1 = 3; q = 2; 3, 6, 12, 24, 48, ...; a_1 = -2; q = -4; -2, 8, -32, 128, -512, ...; a_1 = 9; q = 1/3; 9, 3, 1, 1/3, 1/9, ...; a_1 = 2; q = 1; 2, 2, 2, 2, 2, ... The general formula for the nth term of an geometric sequence: a_n = a_1 * q^{n-1}. The sum of the first $n$ term of an geometric sequence: S_n = a_1 * 1-q^n / 1-q; for q = 1 S_n = n * a_1. The property of an arithmetic sequence: a_n^2 = a_{n-1} * a_{n+1}.