Question

The sum of consecutive integer numbers is 50. How many numbers are there?​

Answer 1

Step-by-step explanation:

Sum of 2 consecutive integers is always an odd number and 50 being even, we can’t find 2 consecutive intergers to sum up to 50.

Sum of 3 consecutive integers is always divisible by 3 and 50 being not divisible by 3, we can’t find 3 consecutive intergers to sum up to 50.

Sum of 4 consecutive integers is always an even number not divisible by 4 and 50 being even and not divisible by 4, we can find 4 consecutive intergers to sum up to 50. Indeed, the integers are 11, 12, 1 3 and 14.

Sum of 5 consecutive integers is always divisible by 5 and 50 being divisible by 5, we can find 5 consecutive intergers to sum up to 50. Indeed, the integers are 8, 9, 10, 11 and 12.

Sum of 6 consecutive integers is always divisible by 3 and since 50 is not such a number, we can’t find 6 consecutive integers to sum up to 50.

Sum of 7 consecutive integers is always divisible by 7 and 50 is not a muliple of 7, so there can’t be 7 consecutive integers to give you 50.

Sum of 8 consecutive integers is always divisible by 4 and 50 being not a multiple of 4, so there can’t be 8 consecutive integers to give you 50.

Sum of 9 consecutive integers is always divisible by 9 and since 50 is not a multiple of 9, there can’t be 9 consecutive integers to give you 50.

Sum of 10 consecutive integers is never divisible by 10 and since 50 is divisible by 10, there can’t be 10 consecutive integers to give you 50.

For 11, the sum has to be divisible by 11 and 50 is not.

For 12, the sum has to be divisible by 6 and 50 is not.

For 13, the sum has to be divisible by 13 and 50 is not.

For 14, the sum has to be divisible by 7 and 50 is not.

For 15, the sum has to be divisible by 15 and 50 is not.

…

…

We have few more answers.

Sum of 1 consecutive integer can give you 50 and the integer is 50.

Since we are talking about integers, negative integers should be OK and thus we have 3 more answers, as per below:

-7, -6, -5, … 5, 6, 7, 8, 9, 10, 11 and 12 (20 consecutive integers, giving you sum 50)

-10, -9, … 9, 10, 11, 12, 13 and 14 (25 consecutive integers, giving you 50)

-49, -48, … 48, 49 and 50 (100 consecutive integers, giving you 50)

Thus, you have 6 answers:

50 (1 consecutive integer, giving you 50)

11, 12, 13 and 14 (4 consecutive integers, giving you 50)

8, 9, 10, 11 and 12 (5 consecutive integers, giving you 50)

-7, -6, -5, … 5, 6, 7, 8, 9, 10, 11 and 12 (20 consecutive integers, giving you sum 50)

-10, -9, … 9, 10, 11, 12, 13 and 14 (25 consecutive integers, giving you 50)

AND

-49, -48, … 48, 49 and 50 (100 consecutive integers, giving you 50).