An auditorium with 52 rows is laid out where 6 seats comprise the first row, 9 seats comprise the second row, 12 seats comprise the third row. the number of seats increases by 3 per row. what is the seating capacity of the auditorium.
a) 4,290
b) 4,368
c) 1,508
d) 4,160

Answers

The number of seats per row generate an arithmetic sequence. Let a_n denote the number of seats in the n-th row. We're told that the number of seats increases by 3 per row, so we can describe the number of seats in a given row recursively by

\begin{cases}a_1=6\\a_n=a_{n-1}+3&\text{for }2\le n\le52\end{cases}

The total number of seats is given by the summation

\displaystyle\sum_{n=1}^{52}a_n

Because a_n is arithmetic, we can easily find an explicit rule for the sequence.

a_n=a_{n-1}+3
a_n=(a_{n-2}+3)+3=a_{n-2}+2\cdot3
a_n=(a_{n-3}+3)+2\cdot3=a_{n-3}+3\cdot3
\cdots
a_n=a_1+(n-1)\cdot3

So the number of seats in the n-th row is exactly

a_n=6+(n-1)\cdot3=3+3n

This means the total number of seats is

\displaystyle\sum_{n=1}^{52}a_n=\sum_{n=1}^{52}(3+3n)=3\left(\sum_{n=1}^{52}1+\sum_{n=1}^{52}n\right)

You should be familiar with the remaining sums. We end up with

\displaystyle\sum_{n=1}^{52}a_n=3\left(52+\dfrac{52\cdot53}2\right)=4290
B , just multiply and that’s what u get
B because if u multiply it that is what u will get so just multiply it


Do you know the answer?

Other questions on the subject: Mathematics

Mathematics, 21.06.2019, jetblackcap
The answer is biodiversity resulting from new ancestors....Read More
1 more answers
answer is 8x+24area of vanessa's patio = length × width given, length = (3x² + 5x + 10) width = (x² - 3x - 1) area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1) = 3x²(x² - 3x -...Read More
3 more answers
Hence,a. 12, 144, 1728,..  => Geometricb. 0,5, 10, 15, 20, 25,...  => Arithmeticc. 0,4, 16, 36, 64,...  => Neither arithmetic nor geometricd. 1.5, 2.25, 3.375, 5.0625,......Read More
2 more answers