What's the next number in this number sequence?
What's the next number in this number sequence?
Find the next number in this sequence:
2, 4, 8, 13, 20, 29, 41, ?
EXTENSION:
Find the number for the nth term in the sequence (in terms of n).
Hint:
Fibonacci+Triangle
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The hint has nothing to do with that.
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– ThyrsoidMouse73
Sep 9 '18 at 2:34
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Ok, just checking
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– Duck
Sep 9 '18 at 2:35
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And I changed it to make it more obvious.
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– ThyrsoidMouse73
Sep 9 '18 at 2:37
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OEIS found this but I don't think that is what you had in mind
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– Bennett Bernardoni
Sep 9 '18 at 2:45
2 Answers
2
I think the answer is
57
Solution for the extension :
$$Fi. Δ.$$
$$1 + 1 = 2$$
$$1 + 3 = 4$$
$$2 + 6 = 8$$
$$3 + 10 = 13$$
$$5 + 15 = 20$$
$$8 + 21 = 29$$
$$13 + 28 = 41$$
$$21 + 36 = 57 leftarrow (Next Term)$$
Round off to the nearest integer.
$Fi(n) = roundbiggl(frac(-frac1phi)^nsqrt5biggr)$
$Delta(n) = fracn(n + 1)2$
$int(n) = Fi(n) + Delta(n) = roundbiggl(frac(-frac1phi)^nsqrt5biggr) + fracn(n + 1)2$
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Yes, good job!!
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– ThyrsoidMouse73
Sep 9 '18 at 7:00
The next number is
$34$
The formula is
$2^n - dfrac(n-1)(n-2)(n-3)2$
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I'm thinking of a different formula and I realized this worked as well so I'll edit the question.
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– ThyrsoidMouse73
Sep 9 '18 at 2:25
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mathworld.wolfram.com/TribonacciNumber.html
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– Duck
Sep 9 '18 at 2:33