My Math Forum Geometric Series Problem

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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: 876 Thanks: 60 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: 876 Thanks: 60 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.

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