Sequences/patterns

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Jeff1801

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Apr 2, 2021
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16
Hi,
Could someone please help me get a start to this question in the image below. I'm not sure how to go about it.
Thanks.
 

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I can’t read the entire attachment. The bits I can see appear to be asking for a proof that a sequence converges. If that is the case, this is posted in the wrong forum.
 
Jeff1801 said:
Hi,
Could someone please help me get a start to this question in the image below. I'm not sure how to go about it.
Thanks.
Click to expand...
Make a table of sellers offers and buyers offers. List 5 consecutive offers/counteroffers.

Show us what you get.

Do you see a pattern ?
 
Subhotosh Khan said:
Make a table of sellers offers and buyers offers. List 5 consecutive offers/counteroffers.

Show us what you get.

Do you see a pattern ?
Click to expand...
I couldn't see any pattern when I tried to list them out. For the buyers offers all I know is that they are less than the sellers offer and the next sellers offer is average of his previous offer and the buyers offer.
 
Jeff1801 said:
I couldn't see any pattern when I tried to list them out. For the buyers offers all I know is that they are less than the sellers offer and the next sellers offer is average of his previous offer and the buyers offer.
Click to expand...
Did you make a table?

Show us the table.
 
Jeff1801 said:
I listed them out. I'll attach it below.
Click to expand...
What does your problem statement say about b2?

s1 → b1 → s2[=1/2 (s1 +b1)] → b2[=1/2(s2+b1)] → s3[=1/2(s2+b2)] → ............................continue [edited]
 
Last edited by a moderator:
Your list is quite small. Go further until YOU see a pattern.

If I write the numbers 1, 2 you can't see one obvious pattern. The pattern can be 1,2,3,4,5,,, or 1,2,4,8,16,32,.. or something else.
 
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