Question

There is an auditorium with 35rows of seat .There are 14 seats in first row ,18 seat s in second row 22 seats in 3 row and so on Find number of seats in 20th row and also find total number of seats in auditorium (please answer step by step and fast)

Answer 1

hey ur answer
___________
a=14
d=4
n=35
no of seat in 20th raw
tn=a+(n-1)d
t20=14+(19*4)=90

total seats in auditorium
total seat= s35=n/2(2a+(n-1)d)=35/2(28+(34*4))
s35=2870

Answer 2

It is a problem of Arithmetic Progression (A.P)
Total no. of rows=n = 35
First term=a = 14
Common Difference=d = 18-14=22-18= 4

Seats in 20th row = a20 = a +19d = 14 + 19*4 = 14+76=90

Therefore there are 90 seats in 20th row
Now
Total no of seats = sum of seats in all rows

Sum of N term in an AP = n/2 (2a +(n-1)d)
Put the values from above
= 35/2 ( 2*14 + 34*4)
= 35/2 ( 28 + 136)
= 35*164/2
= 35 * 82
= 2870

Therefore total no. of seats in the auditorium is 2870.