The sum of 6 consecutive integers is 519.
What is the third number in this sequence?
To find the third number in this sequence, we need to consider the concept of consecutive integers and their sum.
Consecutive integers are a sequence of numbers in which each number follows the previous one by adding 1. For example, 1, 2, 3, 4, and so on.
To find the sum of consecutive integers, we can use the formula: sum = (first number + last number) * (number of terms) / 2.
Let's use this formula to solve the problem.
Let's assume the third number in the sequence is "x". Since there are 6 consecutive integers, we can represent the sequence as x-2, x-1, x, x+1, x+2, and x+3.
Now, let's find the sum of these integers: (x-2) + (x-1) + x + (x+1) + (x+2) + (x+3).
We know that this sum is equal to 519, so we can write the equation as follows:
(x-2) + (x-1) + x + (x+1) + (x+2) + (x+3) = 519.
By simplifying the equation, we can combine like terms:
6x + 3 = 519.
Subtract 3 from both sides of the equation:
6x = 516.
Divide both sides by 6 to solve for x:
x = 86.
So, the third number in the sequence is 86.
n-2 , n-1 , n , n+1 , n+2 , n+3
6 n + 3 = 519