Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

2015 AMC 10A Problems/Problem 7

Revision as of 15:47, 4 February 2015 by Ariel86 (talk | contribs) (Problem and Solution 7)

Problem

How many terms are in the arithmetic sequence 13, 16, 19,..., 70, 73?

$\textbf{(a)}\ 20 \qquad\textbf{(B)} \ 21 \qquad\textbf{(C)} \ 24 \qquad\textbf{(D)} \ 60 \qquad\textbf{(E)} \ 61$


Solution

73-13 is 60, so the amount of terms in the sequence 13, 16, 19,..., 70, 73 is the same as in the sequence 0, 3, 6,..., 57, 60.

In this sequence, the terms are the multiples of 3 going up to 60, and there are 20 multiples of 3 in 60.

However, one more must be added to include the first term. So, the answer is $\boxed{\textbf{(B) }21}$.

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2015_AMC_10A_Problems/Problem_7&oldid=67321"