a theatre has 30 rows of seats. there are 16 seats in the first row and each additional row has 2 more seats than the previous row. Seats are allocated randomly to all theatre patrons. Calculate the probability that a randomly chosen patron will be seated in the last row of the theatre

Question

hero · Answer

gabby, what course are you taking?

campbell_st · Answer

there are several parts to this question

firstly the seating forms an arithmetic sequence

you have a = 16, d = 2 and n = 30

you will need to find the sum of the seats in the theatre

use 

$$s _{n} = \frac{n}{2}[2a + (n -1)d]$$

then you will need to find the number of seats in the 30th row

$$T _{n} = a +(n -1) d$$


this information will be needed for the probability question

P( last row seat) = (number of seats in the last row)/(total number of seats)

hope this helps

anonymous · Answer

I'm taking pre calc sorry for the late response

anonymous · Answer

Yeah it did help thanks ! (: