2015 AMC 10A Problem 7

Attempt Problem 7 of the 2015 AMC 10A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2015 AMC 10A solutions, or check the answer key.

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How many terms are in the arithmetic sequence $13,$ $16,$ $19,$ $\dotsc,$ $70,$ $73?$

$20$

$21$

$24$

$60$

$61$

Answer: B

Concepts:arithmetic sequence

Difficulty rating: 870

Solution:

Recall that the $n$ th term of an arithmetic sequence is $a + d(n - 1),$ where $a$ is the first term and $d$ is the common difference.

For us, $a = 13$ and $d = 3.$ Plugging these in, we get that $\begin{aligned} 73 &= 13 + 3(n - 1) \\ 20&= n - 1 \\ n &= 21. \end{aligned}$ Thus, B is the correct answer.

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