an outdoor theater has 33 seats in the 1st row, 35 in the 2nd, 37 in the 3rd row and so on. there are 32 rows together. how many can the theater seat?

Question

anonymous · Answer

First,use the formula for arithmetic sequence to find the number of seats in the 32nd row.

$$t_{32} = 33 + 2(32-1)$$
$$t_{32} = 95$$

Now, use the formula for arithmetic series (sum) to find the sum of seats in the theater:

$$S_{n}=\frac{ n }{ 2 }(t_{1} + t_{n})$$
$$S_{n} = \frac{ 32 }{ 2 } (33 + 95)$$
$$S_{n} = 2048$$

There are 2048 seats in the theater in total.
Hope this helped!

anonymous · Answer

thank you so much! that helped a lot

anonymous · Answer

No problem!