Table of Contents

## What is the rule for the sum of any four consecutive even numbers?

Sum of First Ten Even numbers

Number of consecutive even numbers (n) | Sum of even numbers (Sn = n (n+1)) | Recheck |
---|---|---|

4 | 4(4+1) = 4 x 5 = 20 | 2+4+6+8=20 |

5 | 5(5+1) = 5 x 6 = 30 | 2+4+6+8+10 = 30 |

6 | 6(6+1) = 6 x 7 = 42 | 2+4+6+8+10+12 = 42 |

7 | 7(7+1) = 7×8 = 56 | 2+4+6+8+10+12+14 = 56 |

**What is consecutive odd positive integers?**

Consecutive odd integers are odd integers that follow each other in sequence. Simply put, if you select any odd integer from a set of consecutive odd integers, then subtract it by the previous one, their difference will be +2 or simply 2.

### When added four consecutive numbers have a sum of 18?

Let, numbers are (2a-3) , (2a-1) , (2a+1) , (2a+3). Numbers are : 1•5 , 3•5 , 5•5 , 7•5 . (2n+1)+(2n+3)+(2n+5)+(2n+7)=18;8n+16=18; 8n=2; n=2/8=1/4=0,25.

**Can a sum have an odd number as a factor?**

Sum = average number of consecutive numbers. This means the sum has an odd number as a factor. But cannot have an odd number as a factor. This proves that an odd number of consecutive numbers cannot add to make .

#### Is the sum of 4 consecutive numbers always even?

The sum of 4 consecutive numbers must be even. To be more specific, the sum of 4 consecutive numbers is always double an odd number (and any number > 6 that is twice an odd number can be written as the sum of 4 consecutive positive integers).

**Is the even number of consecutive numbers always an odd number?**

An even number of consecutive numbers will not have a whole number as an average. The average will be the average of the two middle numbers. So: But if you add two consecutive numbers, the answer is always an odd number. So a sum like this must have an odd number as a factor again – but doesn’t.

## Is the number 13 a sum of consecutive integers?

The number 13 can be expressed as a sum of consecutive positive integers 6 + 7. Fourteen can be expressed as 2 + 3 + 4 + 5, also a sum of consecutive positive integers. Some numbers can be expressed as a sum of consecutive positive integers in more than one way.