Arithmetic and Geometric ProgressionsDate: 10/10/95 at 5:15:49 From: Anonymous Subject: Arithmetic/Geometric Progression In an Arithmetic Progression whose first term and common difference areboth non-zero, U(n) denotes the nth term and S(n) denotes the sum of n terms. If U(6), U(4), U(10) form a Geometric Progression: (i) show that S(10) = 0 (ii) show that S(6) + S(12) = 0 (iii) deduce that U(7) + U(8) + U(9) + U(10) = U(11) + U(12) gsharpe@pioneer.as.edu.au Date: 10/10/95 at 20:37:44 From: Doctor Ethan Subject: Re: Arithmetic/Geometric Progression Hey, Neat problem. I will get you started then let you finish it. First we need some notation. I will use u4 instead of U(4) (to save use of the shift key) Let u1=r Let the common difference be a Then u4 = 3a + r u6 = 5a+r u10 = 9a+r Great. Then let B be the ratio. So B=u4/u6=u10/u4 This will give us the equation (3a + r)/(5a+r) = (9a+r)/(3a+r). You can check that this solves to 4a(9a+2r)=0 But a can't be zero(see given) so it means that 9a + 2r = 0., Now see if you can use that to solve the problems. If not write back and I will do one for you. -Doctor Ethan, The Geometry Forum |
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