business mathematics

Quantities are said to be in geometric progression when they increase or decrease by a constant factor to get the next or previous term respectively.

This can be represented by a, ar , ar^2, ar^3............ where 'a' is the first term and 'r' is the common ratio of the geometric progression. The n th term of the geometric progression is ar^(n-1)

Sum of all terms is: a(1-r^n)/(1-r)
= (r * last term - first term)/(r-1)

If three terms are in geometric progression, then the middle term is the geometric mean of the other two terms.
Geometric Mean = (abc)^(1/3)
where a, b, c are in geometric progression

similarly, if n terms a1, a2, a3, …….., an are in G.P then
geometric mean = (a1*a2*a3*a4...an)^(1/n)