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smc

geometry senior

Problem

A number of linked rings, each cm thick, are hanging on a peg. The top ring has an outside diameter of cm. The outside diameter of each of the outer rings is cm less than that of the ring above it. The bottom ring has an outside diameter of cm. What is the distance, in cm, from the top of the top ring to the bottom of the bottom ring?
problem
(A)
(B)
(C)
(D)
Solution
The inside diameters of the rings are the positive integers from to . The total distance needed is the sum of these values plus for the top of the first ring and the bottom of the last ring. Using the formula for the sum of an arithmetic series, the answer is .
Final answer
B