In an AP, if the common difference (d) is -4, and the seventh term (a_7) is 4, then find the first term.

The formula for the nth term of an arithmetic progression (AP) is given by:

a_n = a_1 + (n-1)d

where:

a_n = nth term
a_1 = first term
d = common difference
n = number of terms

In this problem, we are given:

d = -4
a_7 = 4
n = 7

We need to find a_1. Substituting the given values into the formula, we get:

4 = a_1 + (7-1)(-4)
4 = a_1 + 6(-4)
4 = a_1 - 24
a_1 = 4 + 24
a_1 = 28

Therefore, the first term (a_1) is 28.