Question 766248
I really need help solving the following problem. An outdoor amphitheater has 29 seats in the first row, 31 in the second row, 33 in the third row, and so on. There are 36 rows altogether. How many can the amphitheater seat?


The last row (36th row) has 99 seats


Formula for the sum of an arithmetic series: {{{S[n] = (n/2)(a[1] + a[n])}}}, where:


{{{S[n]}}} is the sum of the terms, or sum of rows, which is sum of 36 rows


n = number of terms (rows) in the series, which is 36


{{{a[1]}}} = 1st term, or amount in 1st row, which is 29


{{{a[n]}}} = nth term, or in this case, the 36th, or last term, which has 99 seats


{{{S[n] = (n/2)(a[1] + a[n])}}} then becomes:  {{{S[36] = (36/2)(29 + 99)}}} ----- {{{highlight_green(2304)}}} seat-capacity


You can do a manual check, or use excel to do it!!!