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What is Geometric Progression : A series in which each preceding term is formed by multiplying it by a constant factor is called a Geometric Progression G. P. The constant factor is called the common ratio and is formed by dividing any term by the term which precedes it. In other words, a sequence, a1, a2, a3, , an, is called a geometric progression If an+1/an = constant The General form of a G. P. with n terms is a, ar, ar^2 ar ^(n -1) |
| General Term if a = the first term r = the common ratio, T(n) = nth term and S(n) = sum of n terms General term of a GP is Tn = ar ^ (n-1) |
| Sum of first n terms of G.P Sn = a{(r^n)-1}/(r-1) where r >1 Sn = a{1-(r^n)}/(1-r) where r <1 Sn = na where r =1 Sum of infinite G.P: If a G.P. has infinite terms and - 1 < r < 1 or x < 1, Sum of infinite G.P is S8 =a/(1-r) |
| Geometric mean: Three non-zero numbers a, b, c are in G.P. If b^2 = ac or b = Sqrt(ac) b is called the geometric mean of a & c |
