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What is the formula for sum of n terms of G.P |
Answer» Sn=a[r^n-1]/r-1<br>Let ‘a’ be the first term and ’r’(≠) be the common ratio of the given G.P.The general teams of G.P. If Sn\xa0denotes the sum of ‘n’ terms, then,Sn\xa0= a((1 - rn)/(1 - r)) r\xa0≠\xa01This can also written asSn\xa0= a((rn\xa0- 1)/(r - 1))Note: (1) Sn\xa0= a + ar + ar2\xa0+….. +arn-1\xa0(2) If r = 1, then Sn\xa0= a + a + a +……………+a – na\xa0(3) If r = 1, then formulas for Sn\xa0fail\xa0(4) If r < 1, then use Sn\xa0= a((1 - rn)/(1 - r))(5) If r > 1, use Sn\xa0= a((rn\xa0- 1)/(r - 1))(6) Sum of an infinite G.P.,a + ar + ar2 + ..... is a/(1 - r), - 1 r < 1(7) If a, b, c are in G.P.then ‘b’ is the G.M. (geometric mean) between a and c, then b2 = ac\xa0⇒ b =\xa0√ac(8) If A and G are A.M. and G.M. of two given distinct positive real numbers, then relation between A and G is A > G. | |