Question

An auditorium has 51 rows of seats. The first row contains 70 seats. As you move to the rear of the auditorium, each row has 6 more seats than the previous row.
1. How many seats are in row 12 ,136?
2. How many seats are in the auditorium?

Answer 1

Answer:

seats are in row 12 is 136

seats are in row 136 is 880

seats are in the auditorium is 1071000

Step-by-step explanation:

given data

rows of seat = 51

first row seats =  70

each row seats = 6

to find out

How many seats are in row 12 ,136 and How many seats are in the auditorium

solution

it is AP as 70 , 76 , 82, 88 ............

here A = 70 , d = 6

for n = 12 and 136

so An = a + (n-1)d       .........1

A(12) = 70 + (12-1)6

A(12) = 136

and

A(136) = 70 + (136-1)6

A(136) = 880

and

for total seat we get here Sn for 51 row

Sn = $\frac{n}{2}$ × [ 2a(n-1)d]     ...........2

put here value

Sn = $\frac{51}{2}$ × [ 2(70)(51-1)6]  

Sn = 1071000