# Formulas For Geometric Progression

## Geometric Progression Formulas

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. Geometric Progression Formulas is Very important to Solve Questions in less Time.

In this Page Geometric Progression Formulas is given that will help in you solving Different types of problems.

### Formulas for GP

• Common ratio :

Formula for finding the common ratio
$\mathbf{\frac{a_{2}}{a_{1}}}$

• nth term of an GP:

Formula for finding the nth term of an GP $a_{n} = a_{1}r^{n-1}$ where $a_{1}$ = First Term,

r = common ratio and

n = number of Terms

• Sum of first n terms in an GP:
Standard Formula for sum of first n terms in an GP
$\mathbf{\frac{a_{1}(r^{n} -1)}{(r-1)}}$        { if r>1} where, r = common ratio, $a_{1}=$ First Term, n = number of terms
$\mathbf{\frac{a_{1}(1-r^{n}) }{(1-r)}}$        { if r<1} where, r = common ratio, $a_{1}=$ First Term, n = number of terms
• Sum of an infinite GP :

Formula for Sum of an infinite GP

$\mathbf{\frac{a}{1-r}}$                     (if  -1<r<1)

• Geometric Mean (GM) : If two non-zero numbers a and b are in GP, then there GM is GM = $\mathbf{(ab)^{\frac{1}{2}}}$

If three non-zero numbers a,b and c are in GP, then there GM is GM = $\mathbf{(abc)^{\frac{1}{3}}}$

### 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 $\mathbf{\frac{l}{r^{n-1}}}$
• 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.