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So the interesting thing about sequences is that there can be multiple solutions, and you can almost never "prove" without additional information what the "next" value is going to be.

However, in sequences like yours, we can take very good guesses. I think you have a mistake in the last number of your sequence, if 55 is supposed to be 53, then the next value in your sequence is going to be 86. How do we know this? Given the first two values being 6 and 7, every future value will be the sum of the previous two values.

If you want to get all technical, this is called a recursive function, because the next value is dependent on previous values of the function.

In your case f(x) = f(x-1) + f(x-2) given f(0) = 6 and f(1) = 7


f(0) = 6

f(1) = 7

f(2) = 6 + 7 = 13

f(3) = 7 + 13 = 20

f(4) =13 + 20 = 33

f(5) = 20 + 33 = 53

f(6) = 33 + 53 = 86

If you didn't make a typo, and your last value really is 55, then we can still solve it, however we get a significantly more complicated recursive equation (and given the small number of values there is virtually no way to justify one recursion over another) hence why I think you have a typo.

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6y ago
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Q: What is the next number in the sequence 6 7 13 20 33 55?
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