Question

A theater has 29 seats in the first row, 42 seats in the second row, 45 seats in the third row, and so on.
a. Can the number of seats in each row by modeled by an arithmetic or geometric sequence?
a. Write the general terms for a sequence a n that gives the number of seats in row n.
c. How many seats are there in row 19/

Answer 1

It would make more sense if the first row had 39 seats. Because then each row is 3 seats more than the previous row. But even if that isn't the case, the fact that it tells you 'and so on' says that each successive row is longer by three seats.

Answer 2

Your nth row is the sum of your first row and the product of the n-1 st row times the difference.

So, \[a _{n}=a _{1}+(n-1)d\]

Answer 3

oh that lovely formula =l

Answer 4

Yes, but we know all the values of that lovely formula but one. We know n, we know d, and we know a1, so the only thing we don't know but can find is an.

Answer 5

a1 is the 29 correct? and d = 19

Answer 6

Yes, a1 is correct, but your d is not. d is the change in the number of seats for each row after the 1st So, from the second to the third row, the number of seats changed by ?

Answer 7

so an= 29+(n-1)3

Answer 8

Good! That is your general formula. Now, to calculate the number of seats for the 10th row, you just let n=10 and find a10. Since you want to find the number or chairs in the 19th row, n= ?

Answer 9

of*

Answer 10

19?

Answer 11

yep..

Answer 12

an=29+18*3

Answer 13

an=83

Answer 14

a19=29+18*3

Answer 15

Remember, your n=19, so make sure you replace all your n's with 19.

Answer 16

But, other than tha, you are correct. The 19 th row has 83 seats.

Answer 17

oh okay thank you.

Answer 18

that*

Answer 19

geometric, arithmetic?

Answer 20

When adding to the previous term, it is an arithmetic sequence. When multplying to go from one term to the next , that is a geometric sequence.

Answer 21

okay so an= 29+(19-1)3 ?

Answer 22

no, your nth term must contain the letter n, so back to the formula I posted at the very begininng.

Answer 23

a19=29+18*3

Answer 24

That represents your 19th row.

Answer 25

ok that makes sense.

Answer 26

Good. Glad I made some sense.