New Spec A Level Sequences

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!

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}

Reply 2

Ncodling2017

1

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?

Reply 3

mqb2766

21

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.

Reply 4

ScrewTheExams

13

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. :smile: