2011 AMC 12A Problem 8 — Solution | LIVE by Po-Shen Loh

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2011 AMC 12A Problem 8

Attempt Problem 8 of the 2011 AMC 12A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2011 AMC 12A solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

8.

In the eight-term sequence $A, B, C, D, E, F, G, H,$ the value of $C$ is $5$ and the sum of any three consecutive terms is $30.$ What is $A + H?$

$17$

$18$

$25$

$26$

$43$

Answer: C

Concepts:pattern recognition algebraic manipulation

Difficulty rating: 1190

Solution:

Since $A + B + C = B + C + D = 30,$ we get $D = A,$ and likewise the sequence repeats with period $3.$ Thus $H,$ the eighth term, equals $B.$

From $A + B + C = 30$ and $C = 5,$ we have $A + H = A + B = 30 - 5 = 25.$

Thus, the correct answer is C.

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