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Concept explainers
Seats in an Amphitheater An outdoor amphitheater has 35 seats in the first row, 37 in the second row, 39 in the third row, and so on. There are 27 rows altogether. How many can the amphitheater seat?
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To find: An outdoor amphitheater has 35 seats in the first row, 37 in the second row, 39 in the third row, and so on. There are 27 rows altogether. How many can the amphitheater seat?
Answer to Problem 65AYU
1,647
Explanation of Solution
Given:
Number of seats in the first row .
Number of seats in the second row .
Number of seats in the third row .
Total number of rows .
Formula used:
The th term of an arithmetic sequence can be found by the formula,
(Formula 1)
Sum of the first terms of an arithmetic sequence,
(Formula 2)
Calculation:
From the given data, we get .
To find the number of seats in the 27th row:
(By formula 1)
Therefore, the number of seats in the 27th row .
To find the total number of total number of seats in the amphitheater:
(By formula 2)
Therefore, total number of seats in the amphitheater .
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