If the first of 1000 consecutive whole numbers is odd, their sum must be
a) even b) odd c)prime d) negative
Help?
A) even
thanks
To find the sum of 1000 consecutive whole numbers starting from an odd number, we first need to determine the pattern of the consecutive numbers.
Let's consider the first few odd numbers: 1, 3, 5, 7, 9, and so on. We can observe that each odd number is obtained by adding 2 to the previous odd number.
So, the sequence of 1000 odd numbers can be represented as follows:
1, 1 + 2, 1 + 2 + 2, 1 + 2 + 2 + 2, and so on.
We can simplify this sequence further:
1, 3, 5, 7, 9, ...
Now, let's calculate the sum of these 1000 consecutive odd numbers.
The sum of consecutive numbers can be found using the formula:
Sum = (first number + last number) * number of terms / 2
The first odd number in our sequence is 1, and the last odd number can be calculated as:
last number = first number + (number of terms - 1) * common difference
In our case, the common difference is 2, and the number of terms is 1000.
last number = 1 + (1000 - 1) * 2 = 1 + 1998 = 1999
Now, let's substitute these values into the formula:
Sum = (1 + 1999) * 1000 / 2 = 2000 * 1000 / 2 = 1,000,000
Therefore, the sum of 1000 consecutive odd numbers is 1,000,000.
Looking at the answer options given, the sum 1,000,000 is an even number. Therefore, the correct answer is a) even.