### Brain Teasers

# 2, 5, 12, 31, 86....

Series
Series teasers are where you try to complete the sequence of a series of letters, numbers or objects.

What's the next number in this sequence?

2, 5, 12, 31, 86....

246

249

252

255

258

2, 5, 12, 31, 86....

246

249

252

255

258

### Hint

Three is a magic number!### Answer

The answer is 249.3^0 + 1 = 2

3^1 + 2 = 5

3^2 + 3 = 12

3^3 + 4 = 31

3^4 + 5 = 86

3^5 + 6 = 249

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## Comments

No, it's 249.

I might have gotten the answer if it was listed. The CORRECT answer is 249. Quit posting without double checking your work. 3^3+4=31 NOT 86. And 3^4+5=86 NOT 248. JDNOWAY is right.

I agree with the others this is a poor example of posting any old rubbish.

Aug 31, 2002

It appears that cathalmcabe is well adept at posting any old rubbish. almost all his teasers i have seen up to date are either totally incorrect of contain disputable facts.

2, 5, 12, 31, 86, ...

The differences {a2-a1, a3-a2,a4-a3,a5-a4,...} = {3, 7, 19, 55,... }

Now, {b2-b1, b3-b2, b4-b3} =

{4, 12, 36, ... }

The last sequence is geometric with r=3, making the next term 108. Hence, b5-b4 = 108 ; b5= 163; a6-a5 = 163 , or a6 = 249.

The differences {a2-a1, a3-a2,a4-a3,a5-a4,...} = {3, 7, 19, 55,... }

Now, {b2-b1, b3-b2, b4-b3} =

{4, 12, 36, ... }

The last sequence is geometric with r=3, making the next term 108. Hence, b5-b4 = 108 ; b5= 163; a6-a5 = 163 , or a6 = 249.

With the correction, it's not so bad! I worthwhile little challenge. You can also get the next number using "x3 -1", "x3 -3", "x3 -5", etc

i did this to get 258.

the final number times 2, plus the number before it.

Odd coincidence, or did you plan that?

the final number times 2, plus the number before it.

Odd coincidence, or did you plan that?

Quocalimar, that doesn't even work. 2 x 86 + 31 = 203. Neither does it hold for the other numbers in the sequence.

Or am I misunderstanding you completely?

Or am I misunderstanding you completely?

Good one, I got it after the hint. Except I figured it this way, 3x-1, 3x-3, 3x-5, 3x-7....

Where x is each new number progressively.

Where x is each new number progressively.

Nice, but I had the same solution as above (so 3x-1, 3x-3, 3x-5, 3x-7...).

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