C1 Recursion Sequence help

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HappyHumanist
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#1
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#1
Hello all, been doing some past papers and I'm a bit confused as too why one of my methods isn't working: it's Question 8 on Edexcel C1 June 2007 (see http://www.examsolutions.net/a-level...June/paper.php).

A sequence a1, a2, a3 is defined.

a1 = k
an+1=3an+5 n>1

Where k is a positive integer

You are then asked to calculate the sum of the first four terms. The correct way I've found out now is too simply add them up one by one (e.g. write out a1, a2, a3 and a4 and then just sum them), but I'm a bit confused. I tried to use the formula: Sn=n/2(a+L), where n=4, a=k and l=27k +65 (a4), but this gives me an incorrect answer of 56k + 130. The correct answer is 40k + 90. Why doesn't using this formula work? Any help appreciated.
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m4ths/maths247
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#2
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First question....is it arithmetic?
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HappyHumanist
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#3
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(Original post by m4ths/maths247)
First question....is it arithmetic?
I thought all sequences defined by a recursion relationship were!

The terms are:

a1 = k
a2 = 3k + 5
a3 = 9k + 20
a4 = 27k + 65
Thanks!
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m4ths/maths247
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(Original post by HappyHumanist)
I thought all sequences defined by a recursion relationship were!

The terms are:

a1 = k
a2 = 3k + 5
a3 = 9k + 20
a4 = 27k + 65
Thanks!
By letting k=1 does that help you understand why the use of the formula was not successful?
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HappyHumanist
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#5
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(Original post by m4ths/maths247)
By letting k=1 does that help you understand why the use of the formula was not successful?
I see now, it is not an arithmetic series! I assumed that all recursive relationships automatically were, but I now understand my error. Thank-you!
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TheScallywag
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#6
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#6
You simply add all the terms together for the first part which gives you 40k + 90 then take a factor of 10 out to show it can be divided by 10. 10(4k + 9)
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