If the second differences of a sequence are a constant 2 the first of the first differences is 3 and the first term is 12 find the first five terms of the sequence

1. The second differences are constant at 2, i.e.,
a_{n+2} - 2a_{n+1} + a_n = 2
2. The first of the first differences is 3, i.e.,
a_2 - a_1 = 3
3. Given the first term,
a_1 = 12

From this, we can write out the terms:
a_2 = a_1 + 3 = 12 + 3 = 15

Adding the second difference each time to find the next terms:
a_3 = a_2 + (3 + 2) = 15 + 5 = 20
a_4 = a_3 + (5 + 2) = 20 + 7 = 27
a_5 = a_4 + (7 + 2) = 27 + 9 = 36

So the first five terms are:
12, 15, 20, 27, 36