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CEMC Gauss (Grade 7), 2026

Algebra Difficulty 1.4 Junior Find the answer Canada

In the sequence $43,41,39,37,...,3,1$ , the first term is
$43$ , each term after the first is
$2$ less than the term before it, and
the last term is $1$ . How many terms
are in the sequence?

Pick one

Solution

The sequence contains the integers from $1$ to $43$ inclusive with the even integers
removed. The first even integer removed is $2=2\times1$ . The last even integer removed
is $42=2\times21$ , and so the $21$ even integers between $1$ and $43$ were removed. Thus, the number of
terms in the sequence is $43-21=22$ .

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.