AMC 8 Daily Practice - The Sum of a Finite Arithmetic Series

Complete problem set with solutions and individual problem pages

Problem 6 Easy

An arithmetic sequence has its 3^{\text{rd}} term as 14 and 18^{\text{th}} term as 23. How many of the first 2008 terms are integers?

  • A.

    398

  • B.

    399

  • C.

    400

  • D.

    401

  • E.

    402

Answer:E

Common difference d = \frac{23 - 14}{15} = 0.6.

Integer terms occur when 0.6n \in \mathbb{Z} \implies 0.6 \times 5=3.

In 2008 terms: \left\lfloor \frac{2008-3}{5} \right\rfloor +1 = 402 \text{ integer terms}

Final result: \boxed{402}

Related Problems
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Problem 8 AMC 8 Daily Practice - The Sum of a Finite Arithmetic Series
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