Next term?
Number Theory
Level
3
Find the sum of the next 2 terms in the series -
0,1,1,2,4,7,13,24,?,?
The answer is 125.
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These are the famous Tribonacci Numbers. Heard of Fibonacci? This is exactly like that, but each term is the sum of the previous three instead of the previous two: T n = T n − 1 + T n − 2 + T n − 3 . (not to be confused with the triangular numbers T n , sometimes denoted Δ n as Gauss wrote)
So add the last three numbers to get 7 + 1 3 + 2 4 = 4 4 , 1 3 + 2 4 + 4 4 = 8 1 . Then the sum of those two terms is 4 4 + 8 1 = 1 2 5