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sum of squares of 100 terms of arithmetic progression

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

September 22, 2021
algebraArithmetic Progressionarithmetic sequence

Problem Statement

Consider an arithmetic progression made up of 100100 terms. If the sum of all the terms of the progression is 150150 and the sum of the even terms is 5050, find the sum of the squares of the 100100 terms of the progression.
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