The second term of an arithmetic sequence is 7. The sum of the first four terms of the arithmetic sequence is 12. Find the first term, a, and the common difference, d, of the sequence.

Let a be the first term

Let d be the common difference

a + d = 7

S₄ = 4/2 (2a +3d) = 12

Simultaneous equation:

a+d =7 // x 6
4a +6d = 12

Difference btween these two

6a + 6d = 42

4a +6d = 12

2a = 30

a = 15

d = 7 -a 

thus d = -8, a = 15