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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 to solve Geometric Progression

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


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}


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