GEOMETRIC PROGRESSION

                                                     GEOMETRIC PROGRESSION (GP)

SEQUENCE:  A Sequence is a function whose domain is the set of numbers or a subset of the natural numbers .Here the co-domain is the set of real numbers (complex numbers)

If range is a subset of real numbers then the sequence is called is called real sequence

SERIES: By connecting the terms of a sequence with the mathematical operators ,we get a series.

  PROGRESSIONS:

It is not necessary that the terms of a sequence ,always follow certain pattern ,or they are described by some explicit formula for the nth term.

Those sequences whose terms follow a certain pattern are called progressions .The progressions are of 4 types 

1. ARITHMETIC PROGRESSION

2. GEOMETRIC PROGRESSION

3. HARMONIC PROGRESSION

4.ARITHMETIC -GOEMETRIC PROGRESSION  

           GEOMETRIC PROGRESSION: In Maths ,Geometric Progression(GP) is a type of sequence where each succeeding term is produced  by multipying each preceding term by a fixed number ,which is called common ratio .This progression is also called as Geometric sequence of numbers that follow a pattern .

t1,t2,t3,.....tn are in GP ,if t2/t1=t3/t2 = .....tn/t(n-1)=r

where r is a constant and is called common ratio of the given GP, which cannot be zero.

 QUESTIONS:

1.What is formula of GP?

 Ans. Let 'a' be the first term of a G.P. and 'r' be the common ratio, then the sum of the G.P. can be found out by the following formulae: _Sn = a (rⁿ -1)/ r-1, if r ≠1 and. S_n = an , if r = 1. Sum of infinite terms of a G.P.

2.What is nth term of GP?

Ans. A GP can be written as a, ar, ar2, ar3, and so on. Tn = arn-1 (where a = first term and r = common ratio = Tn/Tn-1) is the nth term of a GP series.

3.What is GP in number series?

Geometric Progression (GP)

A sequence of numbers is called a geometric progression if the ratio of any two consecutive terms is always same. In simple terms, it means that next number in the series is calculated by multiplying a fixed number to the previous number in the series.

4.What is the formula of sum of n terms of GP?

 sum of n terms of GP is given by Sn=a(rn−1)r−1 . The above equation represents the sum of n terms of the given GP.