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?

2011 AMC 12A Problem 8

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In the eight-term sequence

A,

B,

C,

D,

E,

F,

G,

H,

the value of

C

5

and the sum of any three consecutive terms is

30.

What is

A + H?

17

18

25

26

43

Consecutive triples having equal sums forces the sequence to repeat every three terms

H

equals

B,

which means

A + H

is the same as

A + B

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.