Find the sum of the first nine terms of the arithmetic progression if a1 = 7, d = 4.

We are given an arithmetic progression (an) by the first term of the arithmetic progression a1 = 7 and the difference of the arithmetic progression d = 4.

In order to find the sum of the first 9 terms of the arithmetic progression, let us recall the formula for finding it.

Sn = (2a1 + d (n – 1)) / 2 * n;

Let’s write down the formula for finding the first 9 terms of the arithmetic progression:

S9 = (a1 + d (9 – 1)) / 2 * 9;

S9 = (a1 + 8d) / 2 * 9;

Substitute the values specified in the condition and calculate:

S9 = (2a1 + 8d) / 2 * 9 = (2 * 7 + 8 * 4) / 2 * 9 = (14 + 32) / 2 * 9 = 23 * 9 = 207.