Question

There is an auditorium with 25 rows of seats. There are 10 seats in the first row, 12 in the second row, 14 seats in the third row and so on. Find the number of seats in the 20 row and also find how many total seats are there in the auditorium?​

Answer 1

Answer:

48, 580

Step-by-step explanation:

a=10, d=2, n=20

total number of seats in 20 rows=(n/2){2a+(n-1)d}

=(20/2){2x10+(20-1)2}

=10(20+19x2)

=10(20+38)

=10x58

=580

and total number of seats in auditorium=(25/2){2x10+(25-1)2}

=25/2(20+24x2)

=25/2x68

=850

Answer 2

Answer:

If there are 25 rows in an auditorium and 10, 12, and 14 seats in the first, second and third rows respectively, then there are 48 seats in 20 th row and a total of 850 seats in the auditorium.

Step-by-step explanation:

Given

Total number rows = 25 rows

Number of seats in the first row = 10

Number of seats in the second = 12

Number of seats in the third row = 14

This is in the form of an AP

10, 12 ,14 ,16, etc

With the first term (a)=10

Common difference (d) = 2

Number of seats in 20th row = 20th term of the AP

Here, n=20

nth term = a+(n-1)d

=10+(20-1)2

= 10+(19*2)

= 10+38

=48

So there are 48 seats in the 20th row

Total number of seats = Sum of all terms in the AP

Here n= 25

Sum of n terms

$=\frac{n}{2} [2a+(n-1)d]\\\\=\frac{25}{2} [2*10+(25-1)2]\\\\= \frac{25}{2} [20+(24*2)]\\\\= \frac{25}{2} [20+48]\\\\=25*34\\\\=850$

So there are 850 seats in total