the sum of 25 consecutive whole numbers is 1000. what is the smallest of the whole numbers?
First number is a, common difference is 1
sum(25) = 1000
(25/2)(2a + 24(1) ) = 1000
2a + 24 = 80
2a = 56
a = 28
To find the smallest of the whole numbers, we need to determine the starting number of the 25 consecutive whole numbers.
Let's call the starting number "x".
We know that the sum of 25 consecutive whole numbers is 1000, so we can set up an equation using the formula for the sum of an arithmetic series:
Sum = (number of terms / 2) * (first term + last term)
In this case, we have 25 terms.
Substituting the given values, our equation becomes:
1000 = (25 / 2) * (x + x + 24)
Now, let's simplify it:
1000 = (25 / 2) * (2x + 24)
To get rid of the fraction, let's multiply both sides of the equation by 2:
2000 = 25 * (2x + 24)
Next, let's distribute the 25 on the right side:
2000 = 50x + 600
Now, let's subtract 600 from both sides:
2000 - 600 = 50x
Simplifying further:
1400 = 50x
Finally, let's solve for x by dividing both sides by 50:
x = 1400 / 50
x = 28
Therefore, the smallest of the whole numbers is 28.