Question

a theater has 20 rows of seats. if there are 32 seats in the $1^{st}$ row, 35 in the $2^{nd}$, 38 in the $3^{rd}$, and so on, how many seats are there in all?

select one:
a. 1270 seats
b. 109 seats
c. 1210 seats
d. 570 seats

Explanation:

Step1: Identify sequence parameters

First term $a_1=32$, common difference $d=3$, number of terms $n=20$

Step2: Find last row seat count

Use arithmetic sequence formula: $a_n = a_1 + (n-1)d$
$a_{20}=32+(20-1)\times3=32+57=89$

Step3: Calculate total seats

Use sum formula for arithmetic series: $S_n=\frac{n(a_1+a_n)}{2}$
$S_{20}=\frac{20\times(32+89)}{2}=10\times121=1210$

Answer:

C. 1210 seats