Question

There are four consecutive positive odd numbers and four consecutive even numbers. The sum of the highest even number and the highest odd number is 33.what is the sum of all four consecutive odd and even numbers

Answer 1

This mught b ur anss

Answer 2

$Let \: 2x,2x+1,2x+2,2x+3,2x+4,2x+5,2x+6,2x+7\\are \:8 \: consecutive \: numbers$

$2x ,2x +2,2x+4\:and \:2x+6 \:are \: Four \: consecutive \: even \: numbers\: --(1)$

$2x+1 ,2x +3,2x+5\:and \:2x+7 \:are \: Four \: consecutive \: odd \: numbers \: ---(2)$

/* According to the problem given */

The sum of the highest even number and the highest odd number is 33

$2x+6+2x+7 = 33$

$\implies 4x + 13 = 33$

$\implies 4x = 33 - 13$

$\implies 4x = 20$

$\implies x = \frac{20}{4}$

$\implies x = 5$

$Now, Sum \: of \: 4 \: consecutive \:even \\numbers = 2x + 2x+2+2x+4+2x+6 \\= 8x+12\\= 8\times 5 + 12\\= 40 + 12 \\= 52 \: --(3)$

$Now, Sum \: of \: 4 \: consecutive \:odd\\numbers \\= Sum \: of \: 4 \: consecutive \:even \\numbers + 4 \\= 52 + 4 \\= 56 \: --(4)$

Therefore.,

$\red{Sum \: of \: 4 \: consecutive }\\\red{even \:numbers }\green {= 52 }$

$\red{Sum \: of \: 4 \: consecutive }\\\red{odd \:numbers }\green {= 56 }$

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