Missing number in series

WBahn

Joined Mar 31, 2012
24,974
What do you want it to be?

Pick a number and I can determine a fifth order polynomial that will produce that sequence of numbers.

Similarly, there are other functional forms that can be used to generate a host of six-number sequences that would fit that pattern.
 

GopherT

Joined Nov 23, 2012
8,012
What do you want it to be?

Pick a number and I can determine a fifth order polynomial that will produce that sequence of numbers.

Similarly, there are other functional forms that can be used to generate a host of six-number sequences that would fit that pattern.
UnHelpful and undoubtedly obvious to the OP. No way to prove the sequence with that when the textbooks with this type of question are generally looking for a simple rule-based step function rather than a continuous function.
 

GopherT

Joined Nov 23, 2012
8,012
Trolling again, huh?
Just following your lead - you are trolling the OP. Not helpful. When have you ever seen a missing number in a series question ask for a solution via a fifth-order polynomial solution? Trolling doesn't fit a Mod.
 

WBahn

Joined Mar 31, 2012
24,974
UnHelpful and undoubtedly obvious to the OP. No way to prove the sequence with that when the textbooks with this type of question are generally looking for a simple rule-based step function rather than a continuous function.
Then the problem needs to state the bounds on the kind of relationship that is fair game -- which it may well do (by way of context of the material being covered in the section that this problem is associated with). But since I don't have a crystal ball I can't tell that unless and until the TS provides that information.

There is a pretty simple rule-based function that can generate this function involving the cubes of a simpler sequence.
 

WBahn

Joined Mar 31, 2012
24,974
Just following your lead - you are trolling the OP. Not helpful. When have you ever seen a missing number in a series question ask for a solution via a fifth-order polynomial solution? Trolling doesn't fit a Mod.
I'm pointing out information about the lack of information provided. You are just going out of your way to act like an ass. You complain about someone saying something that is "unhelpful and undoubtedly obvious to the TS", which means that, by your own criteria, your post had to be even more "unhelpful and undoubtedly obvious to the TS".

So troll away, I'll respond to the TS, but not to you any longer.
 

WBahn

Joined Mar 31, 2012
24,974
Hello Friends,
how to calculate this :
5205, 3008, x-------,948,605,480

what will be x?
The next two numbers after 480 that the sequence is probably meant to have are 453 and then 452. Focus on those three numbers for a while.
 

GopherT

Joined Nov 23, 2012
8,012
I'm pointing out information about the lack of information provided. You are just going out of your way to act like an ass. You complain about someone saying something that is "unhelpful and undoubtedly obvious to the TS", which means that, by your own criteria, your post had to be even more "unhelpful and undoubtedly obvious to the TS".

So troll away, I'll respond to the TS, but not to you any longer.
Lack of information? Teachers and textbooks have been asking for rule-based solutions to missing numbers in a series questions like this for the past 50 years or more. It is a standard. Why on earth would you expect the OP to provide additional information to a standard. Let me correct myself from above, you are not a troll, you are clueless.

In case you were home-schooled and your mother skipped it, you can review the attached.

https://www.mathsisfun.com/algebra/sequences-finding-rule.html
 
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Thread Starter

ENE

Joined May 5, 2016
6
5205, 3008, x-------,948,605,480

605-480=125
948-605=343
343-125=218
5205-3008=2197

How to think for this series?
 

WBahn

Joined Mar 31, 2012
24,974
5205, 3008, x-------,948,605,480

605-480=125
948-605=343
343-125=218
5205-3008=2197

How to think for this series?
You are on the right track, but one of your numbers is not in keeping with the others.

List the differences between successive numbers in the list. That would be 125, 343, and 2197.

Do you see a pattern in those numbers?
 

WBahn

Joined Mar 31, 2012
24,974
Another way to approach a problem like this -- though like any such method it is not guaranteed to work -- is to plot the known points and see if it looks like a smooth curve could be drawn between them. If so, it is likely that a low degree polynomial can generate that curve.
 

WBahn

Joined Mar 31, 2012
24,974
sorry....?
what this mean?
What if your original list had been:

5205, 3008, x-------,948,605,480,453,452

Do the same thing you did before and see if a pattern is more obvious.

EDIT: Corrected typo in last number.
 
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DGElder

Joined Apr 3, 2016
351
The differences in the sequence are the cubes of a sequence of odd numbers.

605-480=125 is 5^3
948-605=343 is 7^3
x-948 = 729 is 9^3
3008 - x is 11^3
5205-3008=2197 is 13^3

x= 1677

Don't ask me how I did it, no formal method, just trial and error looking for a pattern. And I assume in good faith that the author would not make it too convoluted and should be solvable with integers.
 
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Thread Starter

ENE

Joined May 5, 2016
6
You are on the right track, but one of your numbers is not in keeping with the others.

List the differences between successive numbers in the list. That would be 125, 343, and 2197.

Do you see a pattern in those numbers?
Hello Sir,
I have done it without watching thre next ppost thanks DG..
it is 1677 same as you said to notice pattern.
 

Thread Starter

ENE

Joined May 5, 2016
6
How to make pattern ?
4, 77, 498, 2515, 10076, 30237, .........

77-4=73
498-77=421
2515-4982017
how to solve these type of question in few second ?
 
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