geometric progression
geometric progressionA sequence of numbers such that each is a constant multiple of the one before. For example, a, ar, ar2, ar3,…, arN is a geometric progression (GP). A loan of principal a, with compound interest added annually at 100i per cent, will amount after 1 year to a(1 + i), after 2 years to a(1 + i)2, and after N years to a(1 + i)N. Here r = (1 + i). A geometric progression is convergent, that is, the sum of its first N terms tends to a finite limit a/(1 − r), as N tends to infinity, if −1 < r < 1.
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