In an arithmetic progression, the first term is -5, and the sum of the first seven terms is 28.

In an arithmetic progression, the first term is -5, and the sum of the first seven terms is 28. Find the second term in the progression.

The solution of the problem:

1. Determine the difference of this arithmetic progression using the following formula for the sum of the first n-terms of the arithmetic progression: Sn = (2a1 + (n – 1) * d) * n / 2:

(2 * (-5) + (7 -1) * d) * 7/2 = 28;

(-10 + 6d) * 7 = 56;

-70 + 42d = 56;

42d = 126;

d = 3.

2. Find the second term of the given arithmetic progression:

-5 + 3 = -2.

Answer: The second term of the given arithmetic progression is -2.