CEMC Fermat, 2006

Algebra Difficulty 2.0 Junior Find the answer Canada

In seven term sequence, $5, p, q, 13, r, 40, x$ , each term after the third term is the sum of the preceding three terms. The value of $x$ is

(A) $21$ (B) $61$ (C) $67$ (D) $74$ (E) $80$

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.