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Algebra Difficulty 1.6 Junior Find the answer Canada

When the integers from $17$ to
$352$ are added, the sum is $17+18+19+\cdots+350+351+352=61\,992$ When
the integers from $20$ to $355$ are added, the sum is $20+21+22+\cdots+353+354+355=x$ What is
the value of $x$ ?

Pick one

Solution

The number of integers in the first sum is $352-17+1=336$ .

The number of integers in the second sum is also $355-20+1=336$ .

Each term in the second sum is $3$
more than the corresponding term in the first sum.

That is, $20-17=3$ , $21-18=3$ , $22-19=3$ , and so on to $355-352=3$ .

There are $336$ terms in the second
sum, and each is $3$ greater than the
corresponding term in the first sum, and so the second sum is $336\times3=1008$ greater than the first
sum.

Thus, $x=61\,992+1008=63\,000$ .

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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.