What is the product of 3 consecutive integers?

What is the product of 3 consecutive integers?

If n = 3k + 2, then n + 1 = 3k + 2 + 1 = 3k + 3 = 3(k + 1) which is again divisible by 3. So we can say that one of the numbers among (n, n + 1 and n + 2) is always divisible by 3. Therefore the product of numbers n(n+1)(n+2) is always divisible by 3.

What is the rule for the sum of n consecutive odd numbers?

The formula to find the sum of the first n odd numbers is n x n or n squared. For example, if you plugged 41 in for n, you would have 41 x 41, or 1681, which is equal to the sum of the first 41 odd numbers.

What are three consecutive even integers whose sum is?

Three consecutive even integers can be represented by x, x+2, x+4. The sum is 3x+6, which is equal to 108.

How do you calculate consecutive integers?

Let us call x the smallest integer. Because the next two numbers are consecutive even integers, we can call represent them as x + 2 and x + 4. We are told the sum of x, x+2, and x+4 is equal to 72. x + (x + 2) + (x + 4) = 72.

How do you find three consecutive even integers?

Three consecutive even integers can be represented by x, x+2, x+4. The sum is 3x+6, which is equal to 108. Thus, 3x+6=108. Solving for x yields x=34.

What is the sum of n consecutive even numbers?

Consecutive Numbers Formula The formula for adding n consecutive numbers = [a + (a + 1) + (a + 2) + …. {a + (n-1)}]. Even Consecutive Numbers Formula = 2n, 2n+2, 2n+4, 2n+6,… Odd Consecutive Numbers Formula = 2n+1, 2n+3, 2n+5, 2n+7,…

What is the sum of three consecutive numbers always?

n + (n + 1) + (n + 2) = 3n + 3 3 (n + 3) – this shows indeed that whatever the value of n, the sum of three consecutive numbers will always be divisible by 3 , because it is 3 lots of something. 3 lots of something is a multiple of 3. Even if our first value is n + 1: (n + 1) + (n + 2) + (n + 3) = 3n + 6