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Sagot :
Answer:
400 people attended the air show.
Step-by-step explanation:
Arithmetic sequence:
An arithmetic sequence has the following general equation:
[tex]a_n = a_1 + d(n-1)[/tex]
In which [tex]a_n[/tex] is the nth term, [tex]a_1[/tex] is the first term and d is the common difference between the terms.
The sum of the first n terms of an arithmetic sequence is given by:
[tex]S_n = \frac{n(a_1+a_n)}{2}[/tex]
In this question:
First row 1 seat, second 3 seats, 3rd 5 seats and so on.
So we have the following arithmetic sequence:
{1,3,5,7,9,...}
So [tex]a_1 = 1, d = 9 - 7 = 7 - 5 = ... = 2[/tex]
So
[tex]a_n = 1 + 2(n-1)[/tex]
All 20 rows were filled. How many people attended the air show?
Sum of the 20 terms of the progression. So
[tex]S_{20} = \frac{20(1+a_{20})}{2} = 10(1+a_{20})[/tex]
The 20th term is:
[tex]a_{20} = 1 + 2(20-1) = 1 + 2*19 = 1 + 38 = 39[/tex]
So
[tex]S_{20} = 10(1+a_{20}) = 10(1 + 39) = 10(40) = 400[/tex]
400 people attended the air show.
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