What is the sum of all of the perfect squares between $15$ $15$ and $25$ $25$ , inclusive, minus the sum of all of the other numbers between $15$ $15$ and $25,$ $25,$ inclusive?

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Subject: Pre-Algebra
Focus: Squares

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Answer 1 · 2018-06-14T05:06:37

$- 138$ $-138$

The only perfect squares between 15 and 25 inclusive are $16 and 25$ $16 and 25$

$:.$ Sum of perfect squares $=16+25 = 41$

The sum of the natural numbers between $17 and 24$ is given by:

$S_8 = 8/2(17+24) = 4xx41 =164$

$:.$ Sum of the other numbers $=15+164 = 179$

We are asked for the sum of perfect squares minus the sum of the other numbers:

Sum $= 41-179= -138$