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# Formulas For Geometric Progression

## Formula and Concept For Geometric Progression

If the ratio of any term to its preceding term is constant in a sequence of numbers then the sequence known as Geometric Progression . Geometric Progression is a sequence of numbers where each term except the first is calculated by multiplying the previous one by a fixed, non-zero number called the common ratio ### Formulas for GP

• Common ratio :
Formula for finding the commom ratio

r = a2/a1.

• nth term of an GP :

Formula for finding the nth term of an GP

an = a1rn-1

where

r = common ratio,

a1= first term,

an-1= the term before the nth term,

n = number of terms

• Sum of first n terms in an GP

Standard Formula for sum of first n terms in an GP

Sn = (a1r) /(r-1)        {∴ if r > 1}

and

a1(1-rn)/1-r               {∴ if r < 1}

where, r = common ratio,

a1= first term ,

n = number of terms

• Sum of an infinite GP :

Formula for Sum of an infinite GP

Sn = a/1-r                     (if  -1<r<1)

• Geometric Mean (GM) :

If two non-zero numbers a and b are in GP, then there GM is

GM = (ab)1/2

If three non-zero numbers a,b and c are in GP, then there GM is

GM = (abc)1/3

### Properties of Geometric Progression

• 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 =  a rm-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)).
• Reciprocal of all the term in G.P are also considered in the form of G.P.
• When all terms is GP raised to same power, the new series of geometric progression is form.

Read Also –  Tips and tricks on Geometric Progression