by A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio. For example, the sequence 4, -2, 1, – 1/2,…. is a Geometric Progression (GP) for which – 1/2 is the common ratio.
The general form of a GP is a, ar, ar2, ar3 and so on.
The nth term of a GP series is Tn = arn-1, where a = first term and r = common ratio = Tn/Tn-1) .
The formula applied to calculate sum of first n terms of a GP: S(n) = a ( r^n-1) / r-1
When three quantities are in GP, the middle one is called as the geometric mean of the other two. If a, b and c are three quantities in GP and b is the geometric mean of a and c i.e. b =√ac
The sum of infinite terms of a GP series S∞= a/(1-r) where 0< r<1.
If a is the first term, r is the common ratio of a finite G.P. consisting of m terms, then the nth term from the end will be = arm-n.
The nth term from the end of the G.P. with the last term l and common ratio r is l/(r(n-1)) .
