Question

. A theater has 40 rows of seats, where the first row has 27 seats and each subsequent row has

3 more seats than the previous one. Find the total number of seats in the theater.

Answer 1

number of seats in theater = 1035

Explanation:

Given in question as

Total number of rows of seat = 30

first row contain seat = 20

second row contain seat = 21 .. and so on

This is in arithmetic progression as 20 , 21 , 22 , 23 ...... so on

Then as number of terms N = 30 and first terms = a = 20

so we have to find Tn th terms

So, Tn th terms = first term + ( N -1 ) × d d= common difference i.e 1

Tn th terms = 20 + (30 - 1) × 1

Thus, Tn th terms = 49

i.e The number of seats in 30th row = 49

Now again Total number of seats in theater

sum of Nth terms =

so =

= 15 × 69 = 1035

Hence, Total number of seats in theater = 1035 Answer