calculate a and b if the 2nd difference is 1

Question

3;a;10;b;21

Answer 1

Question: calculate a and b if the 2nd difference is 1. 3;a;10;b;21

      1st difference    2nd difference

21

          (21 - b)

b                                (31 - 2b)

          (b - 10)

10                             (a+b - 20)

          (10 - a)

a                               (13 - 2a)

         (a - 3)

3

All the 2nd differences are equal to 1, giving

31 - 2b = 1

a+b - 20 = 1

13 - 2a = 1

From these simultaneous equations we can see that: a = 6, b = 15