An auditorium has 20 seats in the first row, 24 seats in the second Row, 28 seats in the third row and so on. Then 11. the no. of seats are there in the 16th row is (a) 76 (b) 80 (c) 84 (d) 88 12. in the last row there are 116 seats, then total no. of rows in The auditorium (a) 23 (b) 24 (c) 25 (d) 26
13. total no. of seats in the auditorium is
(a) 1640 (b) 1660 (c) 1680 (d) 1700
14. the hall was full on last Saturday for a show, how much were
Total collection (in rupees) for the day, if each ticket is of
Rs 200
(a) 328000 (b) 332000 (c) 336000 (d) 340000
15. if one seat is added in first row, two seats in second row, three
Seats in third row and so on , then the total no. of seats in the
Auditorium is
(a) 2025 (b) 2000 (c) 1975 (d) 1950
Answers
Answer:
B IS THE WRITE ANSWER
...
Given : An auditorium has 20 seats in the first row, 24 seats in the second Row, 28 seats in the third row and so on.
in the last row there are 116 seats
each ticket is of Rs 200 and Hall was full
To Find : no. of seats in the 16th row
Total no. of rows in The auditorium
total no. of seats in the auditorium
Total collection (in rupees) for the day
if one seat is added in first row, two seats in second row, three
Seats in third row and so on , then the total no. of seats in the Auditorium
Solution
Arithmetic sequence : Sequence of terms in which difference between one term and the next is a constant.
This is also called Arithmetic Progression AP
Arithmetic sequence can be represented in the form :
a, a + d , a + 2d , …………………………, a + (n-1)d
a = First term
d = common difference = aₙ-aₙ₋₁
nth term = aₙ = a + (n-1)d
Sₙ = (n/2)(2a + (n - 1)d)
Sum of Arithmetic sequence (AP) is called Arithmetic series
a = 20
d = 4
16th row n = 16
20 + (16 - 1) 4 = 80
There are b) 80 seats in 16th row.
last row = 116
=> 116 = 20 + (n - 1) 4
=> 96 = (n - 1)4
=> 24 = n - 1
=> n = 25
There are (c) 25 rows in The auditorium
Total number of sets
= (25/2) (20 + 116)
= 1700
total no. of seats in the auditorium (d) 1700
Total collection (in rupees) for the day, = 1700 * 200 = 340000
(d) 340000
Seats Added
1 + 2 + 3 + ... + 25
= (25 ) (26)/2
= 325
total no. of seats in the Auditorium = 1700 + 325 = 2025
(a) 2025
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