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A music festival pavilion has a total of 14 rows of chairs. The first row has 18 chairs and the second row has 22 chairs. In each subsequent row there are 4 more chairs than in the previous row. What is the total number of chairs in the pavilion?

Explanation	Calculations	Help
$We use the Counting Evenly Spaced Integers Rule to count how many rows are from "second row" through "fourteenth row" inclusive.$	$14 - 2 + 1 = 13$	Theory & Tactics Method Card EVEN1-B Click to view full details
$We find how many chairs are in the "fourteenth row" by starting with the 22 chairs in the "second row" and adding 4 chairs twelve times.$	$22 + 12 \times 4 = 22 + 48 = 70$
$We use the Sum of Evenly Spaced Integers Rule to add the chairs from "second row" through "fourteenth row" by multiplying the number of terms by the average of the first and last terms.$	$\frac{13}{2} \times (22 + 70) = \frac{13}{2} \times 92$	Theory & Tactics Method Card EVEN1-D Click to view full details
$We then multiply to find the total number of chairs from rows 2 through 14.$	$\frac{13}{2} \times 92 = 13 \times 46 13 \times 46 = 598$
$Finally, we add the 18 chairs in the "first row" to the total from rows 2 through 14.$	$18 + 598 = 616$

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B

A music festival pavilion has a total of 14 rows of chairs. The first row has 18 chairs and the second row has 22 chairs. In each subsequent row there are 4 more chairs than in the previous row. What is the total number of chairs in the pavilion?

Explanation	Calculations	Help
$We use the Counting Evenly Spaced Integers Rule to count how many rows are from "second row" through "fourteenth row" inclusive.$	$14 - 2 + 1 = 13$	Theory & Tactics Method Card EVEN1-B Click to view full details
$We find how many chairs are in the "fourteenth row" by starting with the 22 chairs in the "second row" and adding 4 chairs twelve times.$	$22 + 12 \times 4 = 22 + 48 = 70$
$We use the Sum of Evenly Spaced Integers Rule to add the chairs from "second row" through "fourteenth row" by multiplying the number of terms by the average of the first and last terms.$	$\frac{13}{2} \times (22 + 70) = \frac{13}{2} \times 92$	Theory & Tactics Method Card EVEN1-D Click to view full details
$We then multiply to find the total number of chairs from rows 2 through 14.$	$\frac{13}{2} \times 92 = 13 \times 46 13 \times 46 = 598$
$Finally, we add the 18 chairs in the "first row" to the total from rows 2 through 14.$	$18 + 598 = 616$

Scroll horizontally to view all columns

B