Arithmetic Series versus Arithmetic Progression

algebra-precalculusdefinitionsequences-and-seriesterminology

AIME 1989/7 says

If the integer k is added to each of the numbers 36, 300, and 596, one obtains the squares of three consecutive terms of an arithmetic series. Find k.

On looking at the solution, it becomes clear that the three terms considered are those of an arithmetic progression:

a, a+d, and a+2d

Shouldn't an arithmetic series be the sum of terms of an arithmetic progression, making it

a, 2a + d, 3a + 3d

Best Answer

The original AIME version of this question, which can be found at https://gogangsa.com/338 , says arithmetic sequence, not arithmetic series. It's not clear how or why the AoPS version changed it, but people do slip up from time to time. The OP is quite correct to question the interpretation of the wording in the version they came across.

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