Question #33e60
2 Answers
Explanation:
Suppose
then
Explanation:
Here is a common way to find the sum of consecutive numbers:
Group it like this way:
Note that, if there are an even number of numbers, then each number will get paired with another one. If, as in this case, there are an odd number of numbers, one number will be left out.
So,
and there are
Let's try to find a more general way to find the sum of consecutive numbers. Notice that when we paired the numbers off, the sum of each pair was equal. Since the first pair is the sum of the smallest and largest number, all of the pairs had a sum equal to the smallest number in the sequence added by the largest number in the sequence.
Now, there are two possible cases. The first case is when the number of numbers is even. Then, all of the numbers are paired together, and the number of pairs is the total number of numbers divided by
But what if the number of numbers is odd? Realize that the number of pairs is still half of the number of numbers. Even though the number of numbers is not divisible by
To summarize, when you have a sequence of consecutive numbers, the sum is half of the total number of numbers, multiplied by the sum of the smallest number in the sequence and the largest number in the sequence.
So,