Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

# find three consecutive odd integers such that the sum of the first and the third equals the sum of the second and 13?

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• If you have 3 consecutive odd integers, the central integer is the mean of the two end integers. Hence the sum of the two end integers is twice the central integer. If the sum is the central integer plus 13, it is obvious the central integer must be 13.

The three integers are 11, 13, 15.

The same argument holds true if the set of integers are consecutive even integers or are any set of integers separated by a constant interval.

Assume the integers are:

n, n+a, n+2a

The sum of the two end integers is n + n+2a = 2n+2a = 2(n+a)

This is obviously double the central integer. The numbers don't even have to be integers. They can be any numbers. The necessary condition is that they be separated by a constant interval.

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• Anonymous
1 month ago

Can you pls restate I didn’t really get that

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• (2n + 1) + (2n + 5) =2n + 3 + 13

4n + 6 = 2n + 16

4n - 2n = 16 - 6

2n = 10

so

2n + 1 = 2(5) + 1 = 11

2n + 3 = 2(5) + 3 = 13

2n + 5 = 2(5) + 5 = 15

the odd integers are: 11, 13,15 ... answer//

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• Three consecutive odd integers such that

the sum of the first and the third equals

the sum of the second and 13:

11, 13. and 15

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• 1st integer = (x + 1)

2nd integer = (x + 3)

3rd integer = (x + 5)

1st integer + 3rd integer = 2nd integer + 13

(x + 1) + (x + 5) = (x + 3) + 13

2x + 6 = x + 16

2x = x + 10

x = 10

1st integer = 10 + 1 = 11

2nd integer = 10 + 3 = 13

3rd integer = 10 + 5 = 15

hope this helps!

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• Let the odd integers be n, n +2, n + 4

n + (n + 4) = (n + 2) + 13

2n + 4 = n + 15

2n - n = 15 - 4

n = 11

The integers are 11, 13 15

Verify

11 + 15 = 26

13  + 13 = 26

FYI

n, n +2, n + 4 works for consecutive even integers as well

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• Let n be the first odd integer.

Let n+2 be the second odd integer.

Let n+4 be the third odd integer.

"The sum of the first and the third..."

n + n+4

"...equals the sum of the second and 13"

n + n+4 = n+2 + 13

2n + 4 = n + 15

2n - n = 15 - 4

n = 11

11, 13, 15

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• Let the first integer be 2n + 1.

Then, the second integer is 2n + 3.

The third integer is 2n + 5.

So, (2n + 1) + (2n + 5) = (2n + 3) + 13

4n + 6 = 2n + 16, or simplify to:

2n + 3  = n + 8

n = 5

so, the first odd number is:

2n + 1 = (2 X 5) + 1 = 11

and the other odd numbers would be 13 and 15

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• (2n+1) + (2n+5) = (2n+3) + 13

4n + 6 = 2n + 16

n = 5

2n+1 = 11

2n+3 = 13

2n+5 = 15

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• let the integers be

2n + 1, 2n + 3, 2n + 5

then 4n + 6 = 2n + 16

==> 2n = 10

==> n = 5

so

11, 13 and 15

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