If the first two numbers in a tribonacci sequence are 5 and 11 and the eighth number is 260, what is the third number?  

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embizze | High School Teacher | (Level 1) Educator Emeritus

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A tribonacci sequence can be defined as `t_n=t_(n-1)+t_(n-2)+t_(n-3)` for `n>4` or as a,b,c,a+b+c,a+2b+2c,2a+3b+4c,...

Here we have 5,11,_,_,_,_,_,260,...

Let the third element be x; then the sequence is:

5,11,x,16+x,27+2x,43+4x,86+7x,156+13x,...

Since `t_8=260` we have `156+13x=260 => x=8`

So the sequence is 5,11,8,24,43,75,142,260,...

Thus `t_3=8` .

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