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Question
There is an auditorium with 27 rows of seats. There are 20 seats in the first row, 22 seats in the second row, 24 seats in the third row and so on. Find the number of seats in the 15th row and also find how many total seats are there in the auditorium?
Solution
Total number of rows = 27
Number of seats in the first row = 20
Number of seats in the second row = 22
Number of seats in the third row = 24
Total number of seats = 20 + 22 + 24 + ..... + upto 27 rows
Here,
a = 20
d = 22 - 20 = 2
We know that, tn = a + (n + 1)d
t15 = 20 + (15 - 1)2
= 20 + 14 × 2
= 20 + 28
t15 = 48
Now S27 = ?
Sn = `n/2 [2a + (n - 1)d]`
S27 = `27/2 [2 xx 20 + (27 - 1)2]`
= `27/2 [40 + 26 xx 2]`
= `27/2 [40 + 52]`
= `27/2 xx 92`
= 27 × 46
S27 = 1242
Hence, the number of seats in the 15th row is 48, and there are 1242 seats in the auditorium.
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