IzzyLJB
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The first three terms of a geometric sequence are:

k+2, 4k, 2k^2, k>0

Find the value of k.

I got k=10 after setting k+2+4k equal to the Sn equation? I worked out r as k/2.

Is this right? Thank you!
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RDKGames
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(Original post by IzzyLJB)
The first three terms of a geometric sequence are:

k+2, 4k, 2k^2, k>0

Find the value of k.

I got k=10 after setting k+2+4k equal to the Sn equation? I worked out r as k/2.

Is this right? Thank you!
Can check it yourself. If r= \frac{k}{2} then obviously the second term should be (k+2) \frac{k}{2} = \frac{k^2}{2} + k but it's not that!

Meaning you did it wrong.

Why not just make the ratios between consecutive terms the same since that must be true on a geo sequence??

I.e. \dfrac{4k}{k+2} = \dfrac{2k^2}{4k}
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Ncodling2017
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Sorry, just found this thread and I’m having problems with the same question. I’d be fine if I could find the common ratio. How can I find the common ratio for that question?
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mqb2766
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(Original post by Ncodling2017)
Sorry, just found this thread and I’m having problems with the same question. I’d be fine if I could find the common ratio. How can I find the common ratio for that question?
I think RDKGames gives you the ratio for the first and second two terms and makes them equal (which it must be for a geometric progression). Simply solve that equation k and check it works.
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ScrewTheExams
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(Original post by Ncodling2017)
Sorry, just found this thread and I’m having problems with the same question. I’d be fine if I could find the common ratio. How can I find the common ratio for that question?
(Original post by mqb2766)
I think RDKGames gives you the ratio for the first and second two terms and makes them equal (which it must be for a geometric progression). Simply solve that equation k and check it works.
(Original post by IzzyLJB)
The first three terms of a geometric sequence are:

k+2, 4k, 2k^2, k>0

Find the value of k.

I got k=10 after setting k+2+4k equal to the Sn equation? I worked out r as k/2.

Is this right? Thank you!
First term in a geometric series is a (k+2 in this question)
Second term is ar (4k in this question)
Third term is ar^2 (2k^2)

Therefore, using basic power laws, and cancelling stuff

ar/a = ar^2 / ar (cancels to r = r)

so

4k / (k+2) = 2k^2 / 4k

Then you simply solve the equation you have formed to find k.


This is very similar to Question 9 on the 2017 C2 paper (old spec) for Edexcel. Have a go at that. I sat that paper.
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kamioooohggy
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can anyone solve this
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A Yee
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k=0 or k=6 I think ?
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But'z dela rosa
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What is the 3 terms geometric sequence of 3, 12, ....
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Gauthmath_Jenny
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