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 September 12th, 2017, 02:46 AM #1 Newbie   Joined: Sep 2017 From: Australia Posts: 4 Thanks: 0 Geometric Series Problem I have a math problem I cannot solve and don't have access to a teacher! Can someone help me? The sum of three consecutive terms of a geometric sequence is 24 and the sum of the next three terms is also 24. Find the sum of the first 12 terms. It may be super easy and I just haven't realized it, idk. Thanks though. P.S. Make it understandable for a Year 11 Student in the top maths please. September 12th, 2017, 02:57 AM #2 Newbie   Joined: Sep 2017 From: Australia Posts: 4 Thanks: 0 Eeeeek, also help with this one if you can please!!! The numbers x, x + 4, 2x + 2 are three successive terms of a geometric sequence. Find the value of x. September 12th, 2017, 03:23 AM #3 Math Team   Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 901 Thanks: 61 Math Focus: सामान्य गणित Sum of first 12 term = 96 Suppose, $\displaystyle a$ is first term and $\displaystyle x$ is the common ratio. Then, $\displaystyle a+ax+ax^{2}=24$ Also, $\displaystyle ax^{3}+ax^{4}+ax^{5}=24$ Solving these, we get $\displaystyle a=8$ and $\displaystyle x=1$. Last edited by skipjack; September 12th, 2017 at 10:56 AM. September 12th, 2017, 03:27 AM #4 Math Team   Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 901 Thanks: 61 Math Focus: सामान्य गणित For the second case, As they are in G.P. $\displaystyle t_{1}×t_{3} = t_{2}^{2}$ $\displaystyle x(2x+2)=(x+4)^{2}$ $\displaystyle x^{2}-6x-16=0$ Either, $\displaystyle x=-2$ or $\displaystyle x=8$ Last edited by MATHEMATICIAN; September 12th, 2017 at 03:29 AM. Tags arithmetic, geometric, problem, sequences, series Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post king.oslo Complex Analysis 0 December 28th, 2014 06:50 AM The Chaz Real Analysis 11 February 7th, 2011 04:52 AM pjigglez Calculus 1 April 18th, 2010 06:22 AM cindyyo Algebra 2 August 24th, 2008 01:25 AM clooneyisagenius Real Analysis 1 January 30th, 2008 12:50 AM

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