By virtue of the Pythagorean Theorem, in a right triangle the sum of the squares of the smaller two sides equals the square of the largest side. Only 9, 12, and 15 fit this rule.
The formula for the sum of n terms in an arithmetic progression is: S = n/2 * (2a + (n-1)d) Here, the common difference, d, is 8 and the first term, a, is 1. Substituting these into the formula, we get:
S = n/2 * (2*1 + 8(n - 1)) S = n + 4n² - 4n S = 4n² - 3n The answer is A.
