SOLUTION: What's the next number in these four sequences... 3, -6, 12, 4, 20, ? 7, 16, 8, 27, 9, ? 2, 7, 26, 101, 400, ? 7, 21, 8, 72, 9, ?

Algebra ->  Sequences-and-series -> SOLUTION: What's the next number in these four sequences... 3, -6, 12, 4, 20, ? 7, 16, 8, 27, 9, ? 2, 7, 26, 101, 400, ? 7, 21, 8, 72, 9, ?      Log On


   

Question 1127290: What's the next number in these four sequences...
3, -6, 12, 4, 20, ?
7, 16, 8, 27, 9, ?
2, 7, 26, 101, 400, ?
7, 21, 8, 72, 9, ?
Found 3 solutions by Alan3354, MathLover1, greenestamps:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
An explanation can be made for any number as the next.
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These problems are a waste of time.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

What's next in these sequences: (and what are the patterns?)
3, -6, 12, 4, 20, ?->
the pattern:

to get from 3 to -6, add %28-9%29
to get from -6 to 12, add+%2818%29)
to get from 12 to 4, add %28-8%29
to get from 4 to+20, add %2816%29
to get from 20 to the next one, add %28-7%29 to get 13
to get from 13 to the next one, add %2814%29 to get 27...
answer: 13+
3, -6, 12, 4, 20, 13


7, 16, 8, 27, 9,?
the pattern
16%2F8+=+2
27%2F9=3
?/10=4
answer: 40

7, 16, 8, 27, 9,40


2, 7, 26, 101, 400, ?
2, 7, 26, 101, 400,?
the pattern ->
2%2A4+-+1=7
7%2A4+-+2=26
26%2A4-3=101
101%2A4-4=400
400%2A4-5=1595
answer:1595
2, 7, 26, 101, 400,+1595+


7, 21, 8, 72, 9,?
the pattern->
7%2A3=21,
8%2A3%5E2=72
+9%2A3%5E3=243
answer: +243
7, 21, 8, 72, 9,243


Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Note that, although tutor @mathlover found patterns that predict certain next numbers for each sequence, those answers are only POSSIBLE right answers. For virtually any sequence, there will be many rules that generate the given sequence; and the different rules are likely to produce different answers for the next number. So any answer anybody gives is only a guess.

If you like recreational mathematics, you can take the time to see IF you can find "A" pattern for a sequence. But there is no way of knowing if the pattern you find is the "right" one, producing the "right" answer.

So, as far as formal mathematics goes, the answer from tutor @alan3354 is right.