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you are sitting in row 23 and notice there are 65 seats in your row. the row in front of you has 63 seats and the row behind you has 67 seats. there are 42 rows in the auditorium. how many seats does the auditorium contain? (hint: find the number of seats in the first and last rows)

Sagot :

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Using the sum of an arithmetic sequence concept, the total number of seats in the hall is 2604

  • Row 23 = 65 seats

The number of seats in a row increases by 2 per row :

  • First row = Row 23 - Row 1 = 22
  • Last row = Row 42 - Row 23 = 19

Number of seats in row 1 = 65 - 2(22) = 65 - 44 = 21 seats

Number of seats in row 42 = 65 + 2(19) = 65 + 38 = 103 seats

Common difference = 2

Using the sum of nth term in a sequence :

Sn = n/2(a + l)

  • a = first term
  • l = last term

Sn = 42/2(21 + 103)

Sn = 21(21 + 103)

Sn = 21(124)

Sn = 2604

Therefore, the total Number of seats is 2604.

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