Question

The sum of five consecutive numbers is 250. What is the difference between the sum of the smallest and the largest number and the square of the middle number?

Answer 1

$Let \: x , (x+1),(x+2),(x+3) \: and \: (x+4) \:are \\five \: consecutive \: numbers$

/* According to the problem given */

$Sum \: of \: 5 \: numbers = 250$

$\implies x+(x+1)+(x+2)+(x+3)+(x+4) = 250$

$\implies 5x + 10 = 250$

$\implies 5x = 250 - 10$

$\implies 5x = 240$

$\implies x = \frac{240}{5}$

$\implies x = 48\: --(1)$

$i) Sum \: of \:the\: smallest \:and \:the \\ largest\: number = x + (x+4)\\= 48 + 48 + 4 \\= 100 \: --(2)$

$ii) Square \:of \:the \: middle \:number \\= (x+2)^{2} \\= ( 48 + 2 )^{2} \\= 50^{2} \\= 2500 \: --(3)$

/* According to the problem given */

$(x+2)^{2} - [ x + (x+4)] \\= 2500 - 100 \\= 2400$

Therefore.,

$\red { Required \: Difference }\green {= 2400}$

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