For The Mathematically Inclined

For The Mathematically Inclined

Anil Saigal
09/24/2009

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?

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?

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Problems from 09/17/09

PROBLEM # 1

Suppose that P = 2^m and Q = 3ⁿ. What is the value of P²ⁿQ^m?

SOLUTION

12^nm.

PROBLEM #2

For k>1, let S_k denote the sum of the k consecutive integers starting with k. Compute the smallest value of k such that S_k is a perfect square.

SOLUTION
81.

Congratulations to Sitaram Chandawarkar, Shakti Goel and Prabhakar Nadkarni, who were the winner of the last set of puzzles.

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