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September 12th, 2017, 03:46 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, 03:57 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, 04:23 AM  #3 
Math Team Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 872 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 11:56 AM. 
September 12th, 2017, 04:27 AM  #4 
Math Team Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 872 Thanks: 60 Math Focus: सामान्य गणित 
For the second case, As they are in G.P. $\displaystyle t_{1}×t_{3} = t_{2}^{2}$ $\displaystyle x(2x+2)=(x+4)^{2}$ $\displaystyle x^{2}6x16=0$ Either, $\displaystyle x=2$ or $\displaystyle x=8$ Last edited by MATHEMATICIAN; September 12th, 2017 at 04:29 AM. 

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arithmetic, geometric, problem, sequences, series 
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