# Geometric Progression (G.P.)

If 'a' is the first term and 'r' is the common ratio, then a G.P. can be written as, aarar2ar3, ........ .
Note that abc are in G. P. â‡” b2 = ac

General term of a G. P. :
General term (nth term) of a G.P. is given by Tn = arnâ€“1

Sum of n terms of a G. P. :
The sum of first n terms of a G.P. is given by
Sn = , when r < 1
or Sn = , when r > 1 and Sn = na, when r = 1

Sum of an infinite G. P. :
The sum of an infinite G.P. with first term a and common ratio r such that | r | < 1,
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Geometric mean (g. m.)
If G be the G.M. between two given quantities a and b then a, G, b, are in G.P.
i.e. â‡’ G2 = ab â‡’ G =