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


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


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


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


This means the total number of seats is


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

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?

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