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Question

Find two consecutive even intergers whose sum is 126?

Find three consecutive odd intergers whose sum is 177?

Find two consecutive even intergers whose sum is 217?

Find four consecutive odd integers whose sum is 8?

Find three consecutive even intergers whose sum is 396?

Answer 1

62 and 64 = 126
57 59 and 61 = 177
no two even integers = 217 ( even + even = even {not odd})
-1 1 3 5 = 9
130 132 134= 396

Answer 2

1. 2n+2n+2=126
4n+2=126
4n=126-2=124
n=124/4
n=32,
therefore your two consecutive integers are 64 and 66

2. 2n-1 +2n+1 + 2n+3 = 177
then 6n +3=177
so, 6n=177-3
so 6n =174
n=174/6=29
therefore your three consecutive odd integers are: 57, 59,61

3. there are no such even integers, since the sum of two even integers is always even, and 217 is NOT even.

4. 2n-1 +2n+1 + 2n+3 +2n+5 = 8
8n+8=8
so 8n=0
n=0
so your integers are: -1, 1, 3, 5

5. 2n+2n+2+2n+4=396
6n+6=396
6n=390
n=65
the integers are 130, 132, 134

Answer 3

set up your equations as follows:

let the first integer be x

consective even/odd numbers that follows: x+2, x+2+2, x+2+2+2, etc.

set up the equations such as x+(x+2) = 126

solve for x and then find the consecutive numbers.

Answer 4

x + (x + 2) + (x + 4) = 126
x + x + 2 + x + 4 = 126
3x + 6 = 126
3x = 120
x = 40

ANS : 40, 42, 44

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x + (x + 2) + (x + 4) = 177
x + x + 2 + x + 4 = 177
3x + 6 = 177
3x = 171
x = 57

ANS : 57, 59, and 61

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x + (x + 2) = 217
x + x + 2 = 217
2x = 215
x = 107.5

You can't have even numbers to find an odd number

I think you mistyped something

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x + (x + 2) + (x + 4) + (x + 6) = 8
x + x + 2 + x + 4 + x + 6 = 8
4x + 12 = 8
4x = -4
x = -1

ANS : -1, 1, 3, 5

You didn't state rather it had to be positive or not.

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x + (x + 2) + (x + 4) = 396
x + x + 2 + x + 4 = 396
3x + 6 = 396
3x = 390
x = 130

ANS : 130, 132, 134

Answer 5

62 and 64

57, 59, 61

can't be done since 2 even number added to gether will be an even number

3, 5

130, 132, 134