Find the sum of the first nine terms of the arithmetic progression if a1 = – 5, d = 3.

To find the sum of the first nine terms of this arithmetic progression, we use the formula for the sum of the first n terms of the arithmetic progression Sn = (2 * a1 + d * (n – 1)) * n / 2 for n = 9, where a1 is the first term of the arithmetic progression, d – the difference of the arithmetic progression.
According to the condition of the problem, a1 = – 5, d = 3, therefore, we can write:
S9 = (2 * a1 + d * (9 – 1)) * 9/2 = (2 * a1 + d * 8) * 9/2 = (2 * (- 5) + 3 * 8) * 9/2 = (-10 + 24) * 9/2 = 14 * 9/2 = 7 * 9 = 63.
Answer: the sum of the first nine terms of this arithmetic progression is 63.