# CLASS-10GEOMETRIC PROGRESSION - INTRODUCTION

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