Find the sum of the arithmetic series 20 + 15 + 10 + ... + (-50).

1. The first term is 20 and the common difference is 15 - 20 = -5. 2. The number of terms is not given, so use a_n = a_1 + (n - 1)d with a_n = -50. 3. That gives -50 = 20 + (n - 1)(-5), so -70 = (n - 1)(-5). 4. Dividing by -5 gives n - 1 = 14, so n = 15. 5. Substitute into S_n = n(a_1 + a_n)/2 to get S_15 = 15(20 + (-50))/2. 6. That is 15(-30)/2 = -450/2 = -225. 7. Using n = 14 instead of 15 would give -210, so counting the terms rather than the steps is what this problem tests. _Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.4 Series and Their Notations_