It is known that the second term of the arithmetic progression is equal to 6

It is known that the second term of the arithmetic progression is equal to 6, and the fifth is equal to 15. What is the difference of this progression?

Any member of the arithmetic progression is calculated by the formula:
(a) n = a1 + d (n-1), where
a1 is the first member of the progression; d-difference of progression; The n-number of the given member.
Then the second term of the progression is:
a2 = a1 + d (2-1);
6 = a1 + d;
The fifth term of the progression is equal to:
a5 = a1 + d (5-1);
15 = a1 + 4d;
We get the system of equations:
6 = a1 + d;
15 = a1 + 4d.
Subtract the other from one equation, then:
6-15 = a1 + d- (a1 + 4d);
-9 = a1 + d-a1-4d;
-9 = -3d;
d = -9: (- 3);
d = 3
Answer: 3