2011 AMC 10A Problem 17

Question

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

Compare two consecutive three-term sums

The sequence repeats every three terms, so

A=D=G

and

C=F

From the condition about the sequence, we get that

A + B + C = 30

B = 25 - A.

Similarly, we get

B + C + D = 30

D = A.

Propagating these values through the sequence and repeating the condition for every consecutive triple, we get that

E = 25 - A, F = 5, G = A,

and finally,

H = 25 - A.

The desired sum is then

A + 25 - A = 25.

Thus, C is the correct answer.

Problem 17 in other years