As level maths sequences

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#1

Getting nowhere with this question, help would be appreciated.
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2 years ago
#2
U1=a, U2=ar, U4=ar^3 from geometric

If they form an arithmetic sequence then U2-U1 = U4-U2
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#3
(Original post by vc94)
U1=a, U2=ar, U4=ar^3 from geometric

If they form an arithmetic sequence then U2-U1 = U4-U2
Right, I got a, ar and ar^3 for geometric and a, ad, 2ad for arithmetic. I'm not sure why you minused them though with u2-u1=u4-u2
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2 years ago
#4
(Original post by Zain786H)
Right, I got a, ar and ar^3 for geometric and a, ad, 2ad for arithmetic. I'm not sure why you minused them though with u2-u1=u4-u2
These 3 terms form an arithmetic sequence, so have the same common difference.
Hence, ar-a = ar^3 -ar
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#5
(Original post by vc94)
These 3 terms form an arithmetic sequence, so have the same common difference.
Hence, ar-a = ar^3 -ar
Apologies for this but you are talking about q7i) right? How does it relate to that question with the proof?
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2 years ago
#6
(Original post by Zain786H)
Apologies for this but you are talking about q7i) right? How does it relate to that question with the proof?
ar-a = ar^3 -ar does simplify to r^3 -2r +1=0
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#7
(Original post by vc94)
ar-a = ar^3 -ar does simplify to r^3 -2r +1=0
I'm sorry but this question has just completely lost me, are we assuming a=1 and I'm still confused why we have a step to minus. I still can't get my head round this lol.
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2 years ago
#8
For an arithmetic sequence: 2nd term - 1st term = 3rd term - 2nd term is always true, it's equal to the common difference d.

Our geometric terms are a, ar and ar^3.
We are told that these form an arithmetic sequence, so from the above:
ar - a = ar^3 - ar
divide both sides by a will give r^3 -2r+1=0 as required.
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#9
(Original post by vc94)
For an arithmetic sequence: 2nd term - 1st term = 3rd term - 2nd term is always true, it's equal to the common difference d.

Our geometric terms are a, ar and ar^3.
We are told that these form an arithmetic sequence, so from the above:
ar - a = ar^3 - ar
divide both sides by a will give r^3 -2r+1=0 as required.
ah right ok I think I get it now thank you, you minus the terms to make them equal to eachother and d, I don't get the significance of the polynomial given in the question and giving a proof though
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