Question

A theater has 30 rows of seats. The 1st row contains 20 sets, the 2nd row contains 21 seats, and so on, each row has one more seat than the previous one. How many seats are there in the theater?

Answer 1

Answer: 1,085

Explanation:

I just divided it into 4 sections; 20’s 30’s 40’s 50’s then I added up the numbers I. Each section, then added those 4 numbers together...

Answer 2

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 =
`(N)/(2) (first term + last term)`

so =
`(30)/(2) (20 + 49)`

= 15 × 69 = 1035

Hence, Total number of seats in theater = 1035 Answer