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Problem 207

Algebra Difficulty 1.4 Multiple choice CEMC Gauss (Grade 8) · Canada · 2024

In the sequence $1, 3, 4, 7,
$\ldots$ , each number beginning with the 4$ is the sum of the two numbers before
it. This means that the next number in the sequence is $4+7=11$ . The smallest number greater than
$100$ that appears in the sequence
is

Pick one

Official solution

Continuing the sequence, we get $1$ , $3$ , $4$ , $7$ , $11$ , $18$ , $29$ , $47$ , $76$ , $123$ , and so the smallest number greater
than $100$ that appears in the
sequence is $123$ .

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