How Do You Do This Question(IN DESCRIPTION)

Question

Consecutive integers are simply integers that follow each other in order.

For example, 1, 2, and 3, are consecutive integers. Algebraically, these consecutive

integers can be represented as follows:

1 - N

2 - N + 1

3 - N + 2

Therefore, the sum of three consecutive integers is written as

N + (N + 1) + (N + 2)

So, consecutive even integers would be represented by N, N + 2, and N + 4,

where N must be an even integer. Consecutive odd integers would also be

represented by N, N + 2, and N + 4, where N must be an odd integer.

1. Find three consecutive even integers whose sum is 48.

2. Find three consecutive odd integers whose sum is 141.

3. Find three consecutive even integers whose sum is –240.

4. Find three consecutive odd integers whose sum is –465.

5. Find three consecutive integers whose sum is 300.

6. Find three consecutive integers whose sum of the first and the third is –88.

7. Find three consecutive integers for which 3 times the sum of the first and the third

integers is –342.

8. Find three consecutive even integers for which –4 times the sum of the first and

the third integers is 192.

Answer 1

1. 3 consecutive even integers are 2n, 2n+2, 2n+4. Sum is 6n + 6 = 48, so 6n = 42, so n = 7. So 14, 16, 18.
2. 3 odd integers. First is 2n+1, then 2n+3 and 2n+5, sum is 6n + 9 = 141 so 6n = 132 so n = 22, so they are 45, 47, 49 total 141
3. use method from 1
4. use method from 2
5. n + n+1 + n+2 = 300 so 3n = 297 so n = 99, so 99,100,101
6. n, n+1, n+2 - n + n + 2 = -88
7. n, n+1, n+2 - 3 ( n + n + 2) = -342
8. n, n+1, n+2 -4 (n + n + 1) = 192