# A Happy New Year! Why don't you solve these questions related to 2018?

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These questions are just for fun. I know the answer of the questions and I will post them after Jan.3.

[Level 1] If the sum of four successive integers is 2018, what are the four integers?

[Level 2] If the sum of more than four successive integers is 2018, what are the all possible sequences?

These questions are just for fun. I know the answer of the questions and I will post them after Jan.3.

[Level 1] If the sum of four successive integers is 2018, what are the four integers?

[Level 2] If the sum of more than four successive integers is 2018, what are the all possible sequences?

##### 3 Answers

#### Explanation:

Let x be the first of the four integers, then the sum of x, x+1, x+2, x+3 is

that's

Then the numbers are

See below.

#### Explanation:

For the level

The sum of

Solving for

but

For negative values we have also

Resuming

Thank you!

#### Explanation:

Here is the answer.

[Level 1]

Let

Four successive integers are

The four integers are

[Level 2]

Let

Then,

Use the formula of arithmetic progression sum.

The product of two integers,

Note that

If

Therefore, the sequences are

and