Answer: 2574 people
Explanation:
The number of seats in each row forms an arithmetic sequence, where each term increases by 2. The formula for the nth term (a_n) of an arithmetic sequence is given by:an=a1+(n−1)⋅dan=a1+(n−1)⋅dwhere:anan is the nth term,a1a1 is the first term,nn is the number of terms,dd is the common difference between terms.In this case:a1=28a1=28 (number of seats in the first row),d=2d=2 (common difference),n=39n=39 (number of rows).Now we can use the formula to find the number of seats in the 39th row:a39=28+(39−1)⋅2a39=28+(39−1)⋅2a39=28+38⋅2a39=28+38⋅2a39=28+76a39=28+76a39=104a39=104So, the amphitheater can seat 104 people in the 39th row.To find the total number of seats, you can use the formula for the sum of an arithmetic series:Sn=n2⋅(a1+an)Sn=2n⋅(a1+an)where:SnSn is the sum of the first nn terms.In this case:n=39n=39 (number of rows),a1=28a1=28 (number of seats in the first row),an=104an=104 (number of seats in the 39th row).S39=392⋅(28+104)S39=239⋅(28+104)S39=19.5⋅132S39=19.5⋅132S39=2574S39=2574Therefore, the amphitheater can seat a total of 2574 people.