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