Use the order of operations to find the value of the expression.

Mathematics

1 answer:

Artyom0805 [142]2 years ago

8 0

Answer: D 44

Step-by-step explanation:

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An auditorium with 52 rows is laid out where 6 seats comprise the first row, 9 seats comprise the second row, 12 seats comprise

ivanzaharov [21]

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

$\displaystyle\sum_{n=1}^{52}a_n=3\left(52+\dfrac{52\cdot53}2\right)=4290$

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Keith_Richards [23]

Answer:

the value of x to the nearest tenth is 12 * x

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