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# Theory of Equations | AIME I, 2015 | Question 1

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2015 based on Theory of Equations.

## Theory of Equations - AIME I, 2015

The expressions A=$1\times2+3\times4+5\times6+...+37\times38+39$and B=$1+2\times3+4\times5+...+36\times37+38\times39$ are obtained by writing multiplication and addition operators in an alternating pattern between successive integers.Find the positive difference between integers A and B.

• is 722
• is 250
• is 840
• cannot be determined from the given information

### Key Concepts

Series

Equations

Number Theory

AIME I, 2015, Question 1

Elementary Number Theory by Sierpinsky

## Try with Hints

First hint

A = $(1\times2)+(3\times4)$

$+(5\times6)+...+(35\times36)+(37\times38)+39$

Second Hint

B=$1+(2\times3)+(4\times5)$

$+(6\times7)+...+(36\times37)+(38\times39)$

Final Step

B-A=$-38+(2\times2)+(2\times4)$

$+(2\times6)+...+(2\times36)+(2\times38)$

=722.

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