Question

A music concert is organized at a memorial auditorium. The first row of the auditorium has 16 seats, he second row has 24 seats, the third row has 32 seats, and so on increasing by 8 each row for a total of 50 rows.
A) Write an equation for the nth term in the arithmetic sequence
B) Using the equation find the number of people that can be accommodated in the 16th row

Answer 1

Answer:

(a)  8n + 8

(b) 136

Step-by-step explanation:

No. of seats in first row = 16

No. of seats in second row = 24

no. of seats in third row = 32

Total number of rows = 50

It forms an arithmetic progression

First term = a = 16

common difference, d = 8

Number of terms, n = 50

(A) The formula for the n th term of an arithmetic progression is given by

Tn = a + (n - 1) d

Tn = 16 + (n-1) 8

Tn = 16 + 8n - 8

Tn = 8n + 8

(B) Now, n = 16

The number of seats in 16 th row is given by

T(16) = 8 x 16 + 8

T(16) = 136 seats

Answer 2

A(n) = 16 + 8(n - 1)

A(16) = 16 + 8(16 - 1)
A(16) = 16 + 120
A(16) = 136 people