What comes next? For 8 year olds. Part II

Question

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.

Answer 1

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

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Notice that

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

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

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

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

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

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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.

Answer 2

The differences between consecutive numbers is increasing:

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

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Sequence of differences:

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

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So my guesses are:

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

and

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

And therefore $$A+B=343$$