. Write the word or phrase that best completes each statement or answers the question.
-A local civic theater has 22 seats in the first row and 21 rows in all. Each successive row contains 3 additional seats. How many seats are in the civic theater?
A) 1070 seats
B) 790 seats
C) 1092 seats
D) 1010 seats

Question

Quizplus · Accepted Answer

This is an arithmetic series where the first term $a = 22$, the common difference $d = 3$, and the number of terms $n = 21$. The sum $S_n$ of an arithmetic series is given by $S_n = \frac{n}{2}[2a + (n-1)d]$. Plugging in the values, we get $S_n = \frac{21}{2}[2(22) + (21-1)3] = \frac{21}{2}[44 + 60] = \frac{21}{2} \times 104 = 21 \times 52 = 1092$.

Write the Word or Phrase That Best Completes Each