Problem

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2016 Shortlist LR3 day1 (logical reasoning)

Tags: algebra, Arithmetic Progression, arithmetic sequence



Consider an arithmetic progression made up of $100$ terms. If the sum of all the terms of the progression is $150$ and the sum of the even terms is $50$, find the sum of the squares of the $100$ terms of the progression.