Question

The sum of 25 consecutive integers is 500 determine the smallest of the 25 integers…

Answer 1

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.

Answer 2

The smallest integer is 8.

Step-by-step explanation:

Let the smallest integer be a.

The sum of 25 consecutive integers is 500.

n = 25, d = 1

Sn = n/2 x (2a + (n-1) x d)

500 = 25/2 x (2a + (25-1) x 1)

500 = 25/2 x (2a + 24)

1000 : 25 = 2 (a + 12)

40 : 2 = a + 12

20 - 12 = a

a = 8