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September 12th, 2017, 02:46 AM   #1
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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.
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September 12th, 2017, 02:57 AM   #2
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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.
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September 12th, 2017, 03:23 AM   #3
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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.
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September 12th, 2017, 03:27 AM   #4
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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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