1963 AHSME Problems/Problem 16
Problem
Three numbers , none zero, form an arithmetic progression. Increasing by or increasing by results in a geometric progression. Then equals:
Solution
Let be the common difference of the arithmetic sequence, so and .
Since increasing by or by results in a geometric sequence, Cross-multiply in both equations to get a system of equations. Rearranging terms results in Substitute and solve for . Finally, substitute and solve for . Since , dividing by is allowed. The answer is .
See Also
1963 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 15 |
Followed by Problem 17 | |
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