Final answer:
To find the smallest of the 25 consecutive integers with a sum of 500, we can use the formula for the sum of an arithmetic sequence. Substituting the given values and solving the equation yields the smallest integer: -2.
Step-by-step explanation:
To find the smallest of the 25 consecutive integers, we can use the formula for the sum of an arithmetic sequence: Sn = (n/2)(2a + (n-1)d), where Sn is the sum, a is the first term, n is the number of terms, and d is the common difference. In this case, the sum is 500 and there are 25 terms. We can substitute these values into the formula and solve for a:
500 = (25/2)(2a + 24)
Dividing both sides by 25 gives:
20 = 2a + 24
Subtracting 24 from both sides gives:
-4 = 2a
Dividing both sides by 2 gives:
a = -2
Therefore, the smallest of the 25 integers is -2.