In the sequence …,a,b,c,d,0,1,1,2,3,5,8,… each term is the sum of the two terms to its left. Find a.

1994 AMC 12 Problem 6

Attempt Problem 6 of the 1994 AMC 12 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 1994 AMC 12 solutions, or check the answer key.

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In the sequence

\ldots,a,b,c,d,0,1,1,2,3,5,8,\ldots

each term is the sum of the two terms to its left. Find

a.

-3

-1

0

1

3

Work backward by subtracting the preceding known term

Determine

d,c,b

in that order before finding

a

Working backward,

d+0=1

gives

d=1,

then

c+d=0

gives

c=-1,

and

b+c=d

gives

b=2.

Finally

a+b=c,

a=-1-2=-3.

Thus the correct answer is A.