An auditorium has 15 seats in the first row, 18 seats in the second row, 21 seats in the third row, and so on for 10 rows. How many seats are there in the auditorium?
A. 285
B. 300
C. 315
D. 330
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An auditorium has 15 seats in the first row, 18 seats in the second row, 21 seats in the third row, and so on for 10 rows. How many seats are there in the auditorium?
A. 285
B. 300
C. 315
D. 330
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Verified answer
Answer:
A. 285
Step-by-step explanation:
[tex]a_{1} = 15\\d = 3\\n = 10\\a_{10} = ?\\S_{10} = ?\\\\a_{n} = a_{1} + (n - 1) d\\a_{10} = 15 + (10 - 1) 3\\a_{10} = 15 + 9 (3)\\a_{10} = 15 + 27\\a_{10} = 42\\\\S_{n} = \frac{n}{2} (a_{1} + a_{n})\\S_{10} = \frac{10}{2} (15 + 42)\\S_{10} = 5 (57)\\S_{10} = 285[/tex]
Answer:
330
Step-by-step explanation:
S10= (10/2)x2(15)+(10-1)x4
S10=5x(30+4x(9)
S10=5x(30+36)
S10=5x66
S10=330