Atheater 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?

number of seats in theater = 1035

Step-by-step 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

t = 3

step-by-step explanation:

put t = 3 in this expression :

(3²-1)(3²-2)(3² - 3)(3² - 4) = 8×7×6×5 = 56×30 = 1680