# the sum of three consecutive odd integers is 237 find integers?

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• 6 years ago
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well you looking for x-2 + x + x+2 = 237

So for anything like this Divide by 3 first and you'll have x as 79. You can figure out the rest.

but imagine say the sum of 4 consective numbers equals 1000.

divide by 5 now = 200 is x

to get x-2, x-1, you just found x, x+1 and x+2

but imagine for a moment x-2 + x+2 is also 400

the same way x-1 + x+1 is also 400

do you see the pattern?

There's a simple enough equation created by not sure if t was John Napier, his teacher asked him to add up all the numbers from 1 to 100, he thought in his mind 1+50 = 2+49 = 3+48.... so 51 x 50 + 5050. All the integers from 1 to 100 added comes out to 5050.

Try another puzzle in your head this time, what are all the numbers from 1 to 20?

Hope that helps, or at least is a little fun

• 6 years ago

Considering x the first number then the others are x+2 and x+ 4

If the sum is 237, then x+ x+2 + x+4 = 237 ==> 3x = 231 ==> x = 77

Then the numbers are: 77, 79, 81 ... it is odd and consecutive... to confirm just find the sum

it is 77+79+81 = 237... OK!

• 6 years ago

77 and 79 and 81.

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