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Problem 620

AMC 10/12, early questions

Algebra Difficulty 3.8 Multiple choice Slovenia — National Math Olympiad · Slovenia

The first term of an arithmetic progression is equal to $\frac{1}{3}$ and the third term is equal to $\frac{1}{5}$ . What is the second term?

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Official solution

The second term of the arithmetic progression is equal to $a_2 = \frac{1}{2}(a_1 + a_3) = \frac{1}{2}\left(\frac{1}{3} + \frac{1}{5}\right) = \frac{4}{15}$ .

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