For The Mathematically Inclined

For The Mathematically Inclined

10/09/2009

PROBLEM # 1
Suppose f(x+3) = 3x² + 7x + 4 and f(x) = ax² + bx + c. What is a+b+c?

PROBLEM #2
Let a + ax + ax² + ax³ +... and a + ay + ay² + ay³ +... be two different infinite geometric series of positive numbers with the same first term. The sum of the first series is x, and the sum of the second series is y. What is x + y?

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Problems from 10/01/09

PROBLEM # 1

The first three terms of an arithmetic sequence are 2x-3, 5x-11, and 3x+1, respectively. The nth term of the sequence is 2009. What is n?

SOLUTION

502.

PROBLEM #2

Convex quadrilateral ABCD has AB = 9 and CD = 12. Diagonals AC and BD intersect at E, AC =14 and triangles AED and BEC have equal areas. What is AE?

SOLUTION
6.

Congratulations to Sitaram Chandawarkar, Dattatraya Joshi, Prabhakar Nadkarni and Bharath Venkataraman, who were the winner of the last set of puzzles.

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