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19 June, 22:18

The numbers of seats in the first 12 rows of a high-school auditorium form an arithmetic sequence. The first row has 9 seats. The second row has 11 seats. a) Write a recursive formula to represent the sequence. b) Write an explicit formula to represent the sequence. c) How many seats are in the 12th row?

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  1. 19 June, 22:27
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    A₁ = 9

    a₂ = 9+2 → a₂ = a₁ + 2. Since it's an AP, d, the common difference is 2

    1) Then the recursive formula is:

    a (n) = a (n-1) + 2

    2) Explicit formula:

    It's an AP, with first term a₁, d = common difference and n = number of term, which is the number of rows in this problem.

    the value of the nth term is given by the formula is:

    value of nth term = a₁ + (n-1). d

    3) Number of seats in the 12th row:

    9 + (12-1).2 = 31 seats
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