What comes next? For 8 year olds. Part II

This question is from the homework of my niece. She is 8 years old. And I could not help her with this question.

There is a sequence of numbers. Problem asks the sum of the next two numbers. And result is one of 232, 311, 343, 434. I couldn't find a rule for the sequence.

7, 10, 15, 23, 34, 53, 83, A, B

A + B = ?


Any ideas?

Spoiler: My best guess is as follows. And I am not sure whether this is the correct rule or the answer.

7 + 10 = 17 AND 17 - 2 = 15 => 2
10 + 15 = 25 AND 25 - 2 = 23 => 2
15 + 23 = 38 AND 38 - 4 = 34 => 4
23 + 34 = 57 AND 57 - 4 = 53 => 4
34 + 53 = 87 AND 87 - 4 = 83 => 4


Therefore

53 + 83 = 136 AND 136 - 4 = 132 = A (4)
83 + 132 = 215 AND 215 - 4 = 211 = B (4)

A + B = 343


But I couldn't explain why the fifth one also uses 4 for the subtraction.

• The differences are $3,5,8=3+5,11=3+8,19=8+11,30=11+19$; $11$ seems to be an odd one! – lab bhattacharjee Oct 7 '14 at 15:38
• I've also noticed that. – Nuri Tasdemir Oct 7 '14 at 15:41
• It is not featured in the OEIS, so it is boring. – mvw Oct 7 '14 at 15:45

Consecutive differences are $$3, 5, 8, 11, 19, 30$$

Notice that

$$3+5 = 8$$ $$3 + 8 = 11$$ $$8 + 11 = 19$$ $$11+19 = 30$$

The next three differences should be $$11 + 30$$ $$30 + (11 + 30)$$ $$(11 + 30) + (30 + (11 + 30))$$

This gives $$A = 83 + 11 + 30 = 124$$ and

$$B = A + 30 + 11 + 30 = 195$$

Finally, we have $$A + B = \boxed{319}$$

I don't like these problems because if you try hard enough, you can find a pattern that justifies anything you want coming next, as in polynomial interpolation.

• Sorry but 319 is not even an answer candidate for the question (result is one of 232, 311, 343, 434). As I told before maybe the question is wrong. And by the way if the differences were 3, 5, 8, 13, 21, 34, it would make sense but this way, I don't know :| – Nuri Tasdemir Oct 7 '14 at 15:49

The differences between consecutive numbers is increasing:

$$7, 10, 15, 23, 34, 53, 83, A, B$$

Sequence of differences:

$$3, 5, 8, 11, 19, 30.$$

So my guesses are:

$$A=83+30+19 = 132$$

and

$$B=A+49+30 =211$$

And therefore $$A+B=343$$

• The problem with this answer is 11. All the other differences are the sum of the two previous ones (Except 3 and 5 of course). As I said before, maybe there is a mistake in the question. I am going to ask to the teacher who gave this question as a homework :) – Nuri Tasdemir Oct 7 '14 at 16:28