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So, this was posted a while ago on another forum site, and so far we have been unable to figure it out:

Two years ago my Calculus teacher gave us a simple number sequence

1 2 4 8 15 30 50 100

and told us to find the next term. He gave us some basic hints.

1. The answer will be less than 150
2. The only "tools" needed are those of a fifth grade math student so Im guessing adding, subtracting, multyplying, dividing etc

Any thoughts?

(Mods: I wasn't sure which forum to post this in, feel free to move it if you think it belongs somewhere else.)
I've found a solution which works I hope:

Take the first two terms and add them then subtract the answer from the third term.

1+2=3, 4-3=1.

Then repeat this however beginning the process on every other term of the sequence.

4+8=12, 15-12=3.

Then 15+30=45, 50-45=5.

As you can see, the final answers you receive (1,3,5) are the odd numbers so hopefully if you found the next answer, you would get 7.

150-x=7, x=143

which is both below 150 and uses very simple maths. (Then for the term after that you double 143 and for the term after that you would use the method I have, and this continues to alternate).
QUOTE (pgrmdave @ Sep 15 2006, 10:25 PM) *
Any thoughts?

My thought are that maths is not for me smile.gif

Sir Psycho Sexy
After about 30 minutes last night at 3am, the answer I came up with was....well 100. I have no idea whether this is the answer, but it is AN answer that works...sorta. Anyway, here's my figurin':

1 * 2 = 2
2 * 2 = 4
4 * 2 = 8
8 * 2 = 16 ...oh dear, but wait! 16 - 1 = 15's a jump, but bear with me
15 * 2 = 30 (yay!)
30 * 2 = 60, the pattern falls apart again, subtract 1 and you get 59, not even close, however subtract 10 (got by multiplying 1 by 10) and you get 50
50 * 2 = 100, now here's the...well, not clever bit, but...
100 * 2 = 200

200 is too big because it's above 150, but that's not the end of it, if you take the same pattern from the previous two cases like this (15 and 50 in the sequence) I subtracted 1 and then 10, following that pattern, I should multiply 10 by 10 and subtract that from the 200 I have, giving me.... 100.

I'm fairly sure this isn't the answer, the treatment isn't consistant to each number in the sequence, but it fits the critera given, and there is a sorta pattern to how it works. Of course, the next 4 numbers would be 200, -800, -1,600, -13,200, which is just a teensy bit ridiculous. tongue.gif

...did I mention I did this at 3am?

Edit: I prefer IATB's answer.
QUOTE (I_am_the_best @ Sep 16 2006, 10:11 AM) *
Take the first two terms and add them then subtract the answer from the third term.

150-x=7, x=143

Surely it would be x-150=7? Which would give x as 157?
I always have been rubbish at progressions. They've never been something that I could see. Somehow my brain just isn't shaped that way. Give me a shape and a piece of paper and I could design a pattern to build the shape with in a single chunk, but sequences of numbers just don't fall into place for me, so I'm with Bryden on this one!
QUOTE (CheeseMoose @ Sep 17 2006, 01:36 PM) *
QUOTE (I_am_the_best @ Sep 16 2006, 10:11 AM) *

Take the first two terms and add them then subtract the answer from the third term.

150-x=7, x=143

Surely it would be x-150=7? Which would give x as 157?

Oaurgh! Man, I was at peace with myself until you have pointed this fatal flaw out. The answer cannot go unkown! We must work harder to discover it.
I think the teacher was having you on you know. On all the web, that sequence only appears on one page:

(PDF file)

And the next step? It's 150.

If it were a recognised sequence then I'm sure it would turn up somewhere.
Did the teacher say less than 150 or did he say 150 or less?
I think I've got an answer, though I don't think it's right. If you divide the numbers into groups of two, making there partner the number next to them you'll get:


The first number in each group is half the number of the other number in the group. This means that the next number in the sequence can be anything, as long as it's not 150 or more, and the number that follows it is double the amount of it.

Don't think that's right, I'll keep working on it. (Or ask my math teacher...)

* Edit* That'd also explain why it's not a reconized sequence, because the number can be virtually anything.
Sir Psycho Sexy
Ok, screw that, I like my solution best, why? Because I made it.
Well, I haven't spent long over it, but its a toughie, and this is stuff I should be able to do fairly well considering the level of maths we study :/
Seems to me that the number 15 is out of place slightly, in that its the only odd number after 1. Still, if there is a pattern of odd-even-even-even-odd-even-even-even-odd, it would at least be uniform. Out of all the stuff I've tried, this seems to make the most sense, so I'm guessing that its at least an odd number, as its the only way I can fit 15 in there at all. Other than that, any pattern in the growth is disrupted entirely by the number 15 :/ It's close to Pat's idea, but the increasing differences (the -1, -10, possible -100) would need to be uniform with the rest of the sequence ie the numbers 1, 2, 4 and 8, which it isn't. So all I can say at the moment is that the answer is most likey odd. I'll work on it some more tomorrow, I guess, and I'll let you know.

p.s. Izzy's analysis is a good one as well, its most likely that the number after the next will be double the next one ie 1 2 4 8 15 30 50 100 x 2x
{Gothic Angel}
It's stupid because it's not an arithmetic or geometric series. And those are the serieseseses I know how to work with laugh.gif

edit: Emma's solution means the final one should be

x= 7+150

rather than 150-x=7 Which doesn't work. I think

edit: Greeneyes has just shattered my pride at figuring that out by pointing out James saw it first. Damn you, James *shakes fist* tongue.gif
The solutions thus far all have their points, but I'm too bad at math to come up with my own. Any word from your teacher?
I have a half worked through possible solution, which I shall finish at some point. Some of the numbers are getting pretty nasty though, so I presume even if it works, it's not the intended one.
Might we be barking up the wrong tree? What if it isn't a mathematical relationship?
^ I was thinking just that in maths. We were posed with the sequence "2, 4, 5, 6, 4, 3..." which has no mathematical solution however (in the theme of european languages day yesterday) if you write the french numbers and count the letters in each number, then you get the sequence.

Perhaps it is something very simple like that. But for the meantime, I cannot think of anything.
The answer to this will probably be yes..but I'm asking to make sure... Does the teacher know the answer???
{Gothic Angel}
My dad, he of the maths degree and infinate knowledge of sequences and all things maths/science/logicy says he's near certain it's not a mathematical relationship. He's going to put it into a wbsite he knows of which is attempting to list every sequence people have ever come up with or something.

Also: The cynic in me is going "Hmmm, I can't find a solution ANYWHERE on the net - what if this is just someone's idea of a joke and it has no solution?"
Co-incidentally, I am now doing sequences in Maths. And I agree with the others, it's probably not a mathematical relationship. Although if it hadn't been specified as less than 150 I would have gone with 157.
If it isn't a mathmatical relationship, then what exactly should we be talking about? Age, language (sharing a common letter or sylable), and maybe even time?
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