The first 40 rows of seating in a certain section of a stadium have 25 seats, 28 seats, 31 seats, and so on. The 41st through the 75th rows each contain 125 seats. Find the total number of seats in this stadium section.

For terms from 1 to 40 you have an arithmetic series, where

a = 25, d=2 and n = 40
sum of those seats = (40/2)(2(25) + 39(2) )
= 2560
then there are 35 rows of 125 seats each or 4375 seats

so we have 6935 seats

To find the total number of seats in this stadium section, we need to calculate the number of seats in each row separately and then sum them up.

For the first 40 rows, we observe that the number of seats in each row forms an arithmetic sequence with a common difference of 3. The first row has 25 seats, so the second row has 25 + 3 = 28 seats, the third row has 28 + 3 = 31 seats, and so on. We can calculate the number of seats in each row using the formula for the nth term of an arithmetic sequence: an = a1 + (n-1)d, where an is the nth term, a1 is the first term, n is the row number, and d is the common difference.

Using this formula, we can find the number of seats in the 40th row:
a40 = 25 + (40 - 1) * 3 = 25 + 39 * 3 = 25 + 117 = 142 seats.

Now, for the rows from 41 to 75, each row has a fixed number of 125 seats. We can simply multiply the number of rows by the number of seats in each row to get the total number of seats in this range:
Number of seats in rows 41 to 75 = (75 - 41 + 1) * 125 = 35 * 125 = 4375 seats.

Finally, to find the total number of seats in the stadium section, we sum up the number of seats in the first 40 rows and the number of seats in rows 41 to 75:
Total number of seats = (25 + 28 + 31 + ... + 142) + 4375.

To find the sum of an arithmetic sequence, we use the formula Sn = n/2 * (a1 + an), where Sn is the sum of the first n terms, a1 is the first term, and an is the nth term.

Using this formula, we can find the sum of the first 40 terms:
S40 = 40/2 * (25 + 142) = 20 * 167 = 3340.

Finally, we can find the total number of seats in the stadium section by summing up the seats in the first 40 rows and the seats in rows 41 to 75:
Total number of seats = 3340 + 4375 = 7715.

Therefore, the total number of seats in this stadium section is 7715.