Give the sum of the greatest five consecutive even numbers less than 700.
well, you know the largest is 698
now write the other 4, and add 'em up.
To find the sum of consecutive even numbers, we need to determine the first term and the number of terms.
The greatest even number less than 700 is 698. Since we need to find the sum of the greatest five consecutive even numbers, we can find the first term by subtracting 4 from 698 (since there are four even numbers between any two consecutive even numbers).
First term = 698 - 4 = 694
Now we have the first term (694) and we know that we need to find the sum of the greatest five consecutive even numbers. This means we need to find the five terms starting from 694.
The sum of consecutive even numbers can be calculated using the formula:
Sum = (n/2)(first term + last term)
Here, n is the number of terms we want to sum up.
In our case, n = 5 (as we want the sum of five consecutive even numbers).
We have the first term (694) and the number of terms (5).
Now, we need to find the last term.
The last term can be found by adding the difference between consecutive terms (which is 2 for even numbers) to the first term, four times.
Last term = first term + (n - 1) * difference
Last term = 694 + (5 - 1) * 2
Last term = 694 + 4 * 2
Last term = 694 + 8
Last term = 702
Using the formula for the sum of consecutive numbers, we can now find the sum:
Sum = (n/2)(first term + last term)
Sum = (5/2)(694 + 702)
Sum = (2.5)(697)
Sum = 1742.5
So, the sum of the greatest five consecutive even numbers less than 700 is 1742.5.