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Definition of a strictly increasing sequence. For every natural n: a_{n+1} - a_n * 0. Examples: 3, 6, 9, 12, ... a_n = 3n; 1, 4, 9, 16, ... a_n = n^2; 1, 3, 5, 7, ... a_n = 2n-1. Definition of a strictly decreasing sequence. For every natural n: a_{n+1} - a_n * 0. Examples: -3, -6, -9, -12, ... a_n = -3n; -1, -4, -9, -16, ... a_n = -n^2; -1, -3, -5, -7, ... a_n = -2n+1.