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Algebra Level 2

An army gained 18 miles of territory on the first day of an invasion. The second day they gained 16 miles, the third day 14, and so forth.

How many miles,in total,did they gain before their invasion was stopped cold?


The answer is 90.

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Denton Young by Denton Young , 47, USA

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2 solutions

Hung Woei Neoh
Jun 1, 2016

18 + 16 + 14 + … + 2 = 2 ( 9 + 8 + 7 + … + 1 ) = 2 ∑ n = 1 9 n = 2 ( 9 ( 10 ) 2 ) = 90 18+16+14+\ldots+2\\ =2(9+8+7+\ldots+1)\\ =2\displaystyle \sum_{n=1}^9 n\\ =2\left(\dfrac{9(10)}{2}\right)\\ =\boxed{90}

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Nice One! (+1)

Samara Simha Reddy - 5 years ago
Denton Young
Jun 1, 2016

Clearly, the gains stopped when they hit 0 miles. The sum up to that point is 18 + 16 + ...+ 2, which can be reorganized as (18 + 2) + (16 + 4) + (14 + 6) + (12 +8) + 10 = 20 + 20 + 20 + 20 + 10 = 90.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

Simple standard appoach.

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