GEOMETRIC PROGRESSION –
A sequence a₁, a₂, a₃,………….,aₑ is called a geometric progression which is supposed to be expressed or written as G.P., if each term is non-zero and
a₂ a₃ a₄ aₑ
----- = ------ = ------ = ………………… = -------- = Constant
a₁ a₂ a₃ aₑ₋₁
The constant ratio is supposed to be called the common ratio.
In a Geometric Progression (G.P.) we shall denote the first term by ‘a’, common ratio by ‘r’, and the e-th term by Tₑ, are called the general term.
Example.1) 4, 8, 16, 32, 64,………… is a G.P. in which a = 4, and
8 16 32 64
r = ------ = ------- = ------- = ------- = 2 (a constant)
4 8 16 32
Example.2) - 6, 18, - 54, 162, - 486,……… Is a G.P. in which a = - 6, and
18 - 54 162 - 486
r = ------- = ------- = ------- = -------- = - 3 (a constant)
- 6 18 - 54 162
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