Question

In a theatre, there are 20seats in the front row and 30 rows were allotted.each successive row contains two additional seats than its front row. How many seats are there ithe ?

Answer 1

Answer:

1470

Step-by-step explanation:

1st term = a= 20

1st term = a= 20no. of terms=n=30

1st term = a= 20no. of terms=n=30common difference=d=2

total seats=n/2{2a + (n-1)d}

=30/2{2×20 + (30-1)×2}

=15{40 + 58} = 15×98 = 1470

Answer 2

The total number of seats in the theater = 1470.

Explanation:

It is given that , 20 seats in the front row and 30 rows were allotted.

Each successive row contains two additional seats than its front row.

i.e. this follows AP with common difference ( d)= 2.

First term = 20

nth term = $a_n=a+(n-1)d$

Sum of first nth terms = $S_n=\dfrac{n}{2}[2a+(n-1)d]$

Number of sets in the theater = $S_{30}=\dfrac{30}{2}[2(20)+(30-1)2]=15(98)= 1470$

Hence, the total number of seats in the theater = 1470.

# Learn more :

there are 25 rows of seats in an Auditorium the first row is of 20seats the second row is of 22 seat the third row is of 24 seat and so on how many seats are there in the 21st floor ​

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