The first term of arithmetic progression is a1=1 and the fourth term is 7. What is the common difference?
We'll recall what is the formula that gives any term of a arthmetic progression:
an = a1 + (n-1)*d
an is the n-th term
a1 is the 1st term
d is the common difference
Since we know the 4th and the 1st terms, we could write:
a4 = a1 + (4-1)*d
7 = 1 + 3d
We'll use the symmetrical property:
3d = 7 - 1
3d = 6
d = 2
The requested common difference of the given arithmetic progression is d = 2.