Question

an auditorium has 36 seats in front row, 40 in the second, 44 in the third and so on....

can the number of seats in each row be modeled by an arithmetic or geometric sequence?

Answer 1

this is an arithmetics series question

as you are adding 4 seats to each row.. and you know the number of seats in the 1st row..

the rows are increasing by the same amount.. so its arithmetic

\[A_{n} = a_{1} + (n -1) \times d\]

you know a1 = 36.. and you can find 4...

this will give the model.

there is a limit on how large n can be... but thats for others to decide.

Answer 2

so ultimately what does an =?

Answer 3

well substitute the values you have... the 1st term 36 and you need to find d, the common difference... which is what is the value that is added to each row to get the next row.

Answer 4

4

Answer 5

its an arithmetic sequence since each time it goes +4

Answer 6

yep so

\[a_{n} = 36 + (n -1) \times 4\]

which can be simplifed

Answer 7

what is it simplified

Answer 8

well distribute (n -1)x 4 =

Answer 9

@higherlearning try it! @campbell_st cant just give you the answer to everything?

Answer 10

4n-4?

Answer 11

a(sub n) = 36 + (n-1)*4 --> see formula stated on attachment

a(sub n) = 36 + 4n - 4 = ? + 4n. n represents the row number and a(sub n) gives the number of seats on row n.

While the number of seats per row in the auditorium appear to form an arithmetic sequence, the sequence would have to be finite. Otherwise, the auditorium would have to have unlimited capacity.

Answer 12

@higherlearning