


Geometric progressionGeometric progression shortly known as GP (also in accurately known as geometric series)is a sequence of numbers such that the quotient of any two successive numbers of the sequence is always a constant. That constant is called as the common ratio of the sequence. a, ar, ar^{2}, ar^{3}, ar^{4},....ar^{n1},... is a GP. Here a or a_{1} is the first term and ris the common ratio. ar is the second term known as a_{2}, ar^{2} is the third term known as a_{3}, .... and ar^{n1} is known as nth term. Example: 3,9,27,81,243,..... Here a=3, r= a_{2}/a = a_{3}/a_{2 = 9/3 = 27/9 =3} Formula to find the nth term of a GP
Example: Find the 25th term of the progression, 2,4,8,16,32,... Solution: a=2, r = 4/2 = 2. a_{25} = 2x2^{251} a_{25} = 2x2^{24} a_{25} = 2x16777216 = 33554432 The sum of Geometric progression: Sum to n terms of a GP means: a+ar+ar_{2}+...ar_{n1} and it is denoted by S^{n}
Sum of infinite geometric serieswhen r<1 is S^{n} = 1/1r which is valid only when r<1 Example: Find S^{10} 200, 100, 50, 25,... Solution: Here a = 200 and r= 100/200 =1/2 = 0.5. So S^{10} = 200(1(0.5)_{10})/10.5 = 200x0.9990234375/0.5 = 199.80468/0.5 = 399.609375 

