Which of the fallowing best completes the sequence 12,8,5, a) 1 b) 2 c)4 d)0

  B) 2

Step-by-step explanation:

The first differences are increasing by 1 from term to term:

8-12 = -4

5-8 = -3

3-5 = -2

2-3 = -1 . . . . . if the next term is 2, as we believe it should be.

Comment on number sequences

Any finite length sequence of n numbers can be modeled exactly by an n-1 degree polynomial. That is, a 4th-degree polynomial can be made to describe the sequence regardless of the next term you may choose.

If you choose the next term to be 2 as we suggest, then the sequence can be modeled by a 2nd-degree polynomial ...

  (n² -11n +34)/2 . . . . for n = 1, 2, 3, ...

341

step-by-step explanation:

all you have to do is 9x31 (which equals 279) and then 20x31 (which equals 620). then you have to subtract. 620-279=341.