Question

An amphitheatro has 17 seats in the first row, 20 in the second, 23 in the third, and so on, for 27 rows. How many seats are in the amphitheatre? The amphitheatre has seats

Answer 1

Answer:

The amphitheatre has;

$1512\text{ seats}$

Explanation:

The number of seats in each row represent an arithemetic sequence;

$17,20,23,\ldots$

since there are 27 rows the number of seats in the last row will be;

$\begin{gathered} a_{27}=a+(n-1)d \\ a=17\text{ first term} \\ d=20-17=3\text{ common difference} \\ a_{27}=17+(27-1)3 \\ a_{27}=95 \end{gathered}$

The sum of all the seats in the amphitheatre will be;

$\begin{gathered} S_{27}=\frac{n}{2}(a+a_{27}) \\ S_{27}=\frac{27}{2}(17+95) \\ S_{27}=\frac{27}{2}(112) \\ S_{27}=1512 \end{gathered}$

Therefore, The amphitheatre has;

$1512\text{ seats}$