Question

a theater is designed with 15 seats in the first row, 19 in the second, 23 in the third, and so on. if this seating pattern continues, how many seats are in the 30th row?

Answer 1

Answer:

131 seats are in the 30th row.

Step-by-step explanation:

The theater is designed with the first row there are 15 seats, in second row 19 seats and in the third row there are 23 seats.

Now, to find the number of seats in the 30th row.

So, we get the common difference($d$) from the arithmetic sequence first:

$19-15=4.$

Thus, $d=4.$

So, the first tem $a(1)$ = 15.

The number of last row ($n$) = 30.

Now, to get the number of seat in the 30th row we put formula:

$a(n) = a(1) + d(n-1)$

$a(30)=15+4(30-1)$

$a(30)=15+4\times 29$

$a(30)=15+116$

$a(30)=131$

Therefore, 131 seats are in the 30th row.