MA170 Lecture Notes - Lecture 7: Discounting, Geometric Progression
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An arithmetic progression or arithmetic series is a sequence of numbers where the di erence between any two successive members of the sequence is a constant. The sum of an arithmetic sequence t1, t2, , tn is given by. A geometric progression or geometric sequence is a sequence of numbers such that the ratio of any two successive terms in the sequence is constant. The nth term in a geometric progression is given by tn = t1rn 1, where r is the ratio of any two successive terms in the sequence (ie. r = tn tn 1. The sum of the rst n terms in a geometric progression is. Sn = t1 + t1r + + t1rn 1 = t1 (1 rn) The sum of the in nite series, t1ri 1 = t1 + t1r + t1r3 + exists (or converges) if and only if |r| < 1.
