Question

There are 30 rows of chairs in an auditorium. There are 24 chairs in the first row, 26 chairs in the 2 nd row, 28 chairs in the 3rd row and so on.
find the total number of chairs in the auditorium.​

Answer 1

First row=20, second row=24, third row=28

So, the A.P is 20,24,28

a=20

d=24−20=4

n=30

S

n

=

2

n

[2×a+(n−1)×d]

S

30

=

2

30

[2×20+(30−1)×4]

=15[40+29×4]

=15[156]

=2340

Total seats are 2340.

Answer 2

Answer:

The number of rows of chairs is 30. The number of chairs in consecutive rows is 24,26,28.... which is an A. P.

Step-by-step explanation:

In the A. P. therefore a = 24, d = -2, n = 30 sn = n/2 [ 2a + ( n - 1 ) d ] therefore S30 = 30/2 [ 2×24 + (30 - 1 ) -2 ] = 30/2 ( 48 + 29 × -2 ) = 30/2 ( -10 ) = 15 × -10 = -150