Question 1162437: My co-worker got this exercise from somewhere regarding number sequences, and we can't figure it out.
6, 78, 85, 8, 17, 24, 10, 34, ??
We can't see a pattern and it feels like we've covered everything out there.
Found 2 solutions by greenestamps, Edwin McCravy:
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
Don't spend too much time on any problem like this; it is IMPOSSIBLE to know the "right" answer.
ANY next number will make a valid sequence.
If a problem like this has an easily discernible answer, then there is a strong LIKELIHOOD that that answer is "right".
But if there is no easily discernible pattern, there is no point in spending more than a minute (at most!) on the problem, since there is no way of knowing whether any answer you come up with is "right".
I spent more time than I should have looking at the sequence while I was typing this response, and I see a possible pattern.
The 6, 8, and 10 by themselves form a nice pattern.
What is left after we account for those is three pairs of consecutive terms:
78 and 85
17 and 24
34 and ??
Since in the first two pairs the difference is 7, perhaps the difference in the last pair is also 7, making the missing number 41.
But that is no more than a guess.........
Answer by Edwin McCravy(20056)  (Show Source):
You can put this solution on YOUR website! But greenestamps, this is the kind of problems they give you on tests to
get a job! It's true, because I remember many years ago when I was
applying for jobs. BTW, I agree with you about the 41.
6, 78, 85, 8, 17, 24, 10, 34
Obviously there is a pattern with term 1,4,7,10,
6, 8, 10,
So we know that the pattern goes:
6, 78, 85, 8, 17, 24, 10, 34, __, 12, __, __, 14
So we need a pattern for
78, 85, 17, 24, 34, __, __, __,
We notice that 85-78=7 and also 24-17=7
So term 3,6,9,12,15,... are 7 more than the terms just before them
So the number after 34 must be 7 more than 34, which is 41
So we have the next term, where your ?? is. Is that all you want?
6, 78, 85, 8, 17, 24, 10, 34, 41
Or do you need to go further? If so you'd need a pattern for
78, 17, 34, __,
So the pattern is:
Terms 1,4,7,10,13 go 6,8,10,12,14,16,...
Terms 2,5,8,11,14 go 78,17,34,129,
which has the pattern:
1. Multiply the number of term by 13
2. Subtract 152.
3. Multiply by the number of term.
4. Divide by 3
5. Add 162
We get that the 2nd term is 78 by
1. Multiplying 2 by 13, getting 26
2. Subtracting 152, getting -126
3. Multiplying by 2, getting -252
4. Dividing by 3, getting -84
5. Adding 162, getting 78, the 2nd term
We get that the 5th term is 17 by
1. Multiplying 5 by 13, getting 65
2. Subtracting 152, getting -87
3. Multiplying by 5, getting -435
4. Dividing by 3, getting -145
5. Adding 162, getting 17, the 5th term
We get that the 8th term is 34 by
1. Multiplying 8 by 13, getting 104
2. Subtracting 152, getting -48
3. Multiplying by 8, getting -384
4. Dividing by 3, getting -128
5. Adding 162, getting 34, the 8th term
It's complicated, but it works.
Edwin
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