finding of a limit L as n → ∞ by putting L = f (L)

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sajeeln97
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I am sooo lost! I found this in the AQA maths specification under "sequences and series" for C2. There are no youtube videos or anything online about finding a limit in sequences and series. can anyone break this down for me? I can't seem to find any past papers that contains a question related to finding such limits either!?

This is the specification (page 38):

http://filestore.aqa.org.uk/subjects...60-W-SP-14.PDF
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RDKGames
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(Original post by sajeeln97)
I am sooo lost! I found this in the AQA maths specification under "sequences and series" for C2. There are no youtube videos or anything online about finding a limit in sequences and series. can anyone break this down for me? I can't seem to find any past papers that contains a question related to finding such limits either!?

This is the specification (page 38):

http://filestore.aqa.org.uk/subjects...60-W-SP-14.PDF
http://filestore.aqa.org.uk/sample-p...W-QP-JAN06.PDF

Question 5, part c.
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sajeeln97
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Thanks RDKGames,
Does anyone know how to solve it? 😅
I know that L is a number which a sequence appears to converge towards but doesn't actually reach that number. I also know that there's some sort of formula for finding L (by replacing the 'Un+1' and 'Un' of a recurring sequence formula with the letter 'L' ) but I have no idea how to solve it to find L? E.g: for question 5, part c that was provided above by RDKGames The formula to find L would be L=pL+q and p is 0.6 and q I believe is 30. The first four terms of that sequence are 200, 150, 120, 102. I think L could be 100 here but I have no idea.. It just appears to be getting smaller towards a certain number.
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RichE
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(Original post by sajeeln97)
Thanks RDKGames,
Does anyone know how to solve it? 😅
I know that L is a number which a sequence appears to converge towards but doesn't actually reach that number. I also know that there's some sort of formula for finding L (by replacing the 'Un+1' and 'Un' of a recurring sequence formula with the letter 'L' ) but I have no idea how to solve it to find L? E.g: for question 5, part c that was provided above by RDKGames The formula to find L would be L=pL+q and p is 0.6 and q I believe is 30. The first four terms of that sequence are 200, 150, 120, 102. I think L could be 100 here but I have no idea.. It just appears to be getting smaller towards a certain number.
You get

L = pL +q.

So just solve for L with your values of p and q. (i.e. make L the subject of that equation).

PS and no L isn't 100
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sajeeln97
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RichE
Yh that's the part I sort of need help on😅L=(0.6)L + (30) how would I solve this for L?
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B_9710
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(Original post by sajeeln97)
RichE
Yh that's the part I sort of need help on😅L=(0.6)L + (30) how would I solve this for L?
It's just a linear equation.
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sajeeln97
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Ok... yh.. I see it now:facepalm2: Thank you everyone.:thumbsup:
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