Question

there is an auditorium with 27 rows of seats.there are 20 seats in the first row,22 seats in the second row,24 seats in the third row and so on.find the number seat in the 15th row and also find how many total seats are there in the auditorium?

Answer 1

Hey!!!!

____________

We have observed that the numbers of seats in each row increase in an AP

Thus in that AP, we have

=> a = 20
=> d = 22 - 20
=> d = 2
=> n = 27(total rows)

To Find : a15 and S27

For part 1, a15 = a + (n - 1)d

=> a15 = 20 + 14(2)
=> a15 = 20 + 28
=> a15 = 48

Thus there are 48 seats in the 15th row.

For part 2

S27 ⤵️

$\frac{n}{2} (2a + (n - 1)d)$

Replacing Values

$= \frac{27}{2} (40 + 26(2))$

$= \frac{27}{2} (40 + 52 )$

$= \frac{27}{2} (92)$

$= 27 \times 46$

$= 1242$

Thus there are 1242 seats in the auditorium

___________

Hope this helps ✌️

Answer 2

hope this help u.......