Question

A theater has 39 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? b. 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

39, 42, 45, ....

What number do you add to 39 to get 42 that you also add to 42 to get 45?

Answer 2

@PECKCE

Answer 3

3

Answer 4

a) Okay, so the sequence appears to be arithmetic with d (common difference) of 3.

b) The nth term (a sub n) = 3n + 36 where n is a positive integer.

If n = 1 , a sub 1 = 3*1 + 36 = 39 which is the number of seats on the first row.

c) Your Task:
Evaluate The nth term (a sub n) = 3n + 36 for n = 19.
Post what you get and we'll compare answers.

Answer 5

a(19)=3(19)+36= 93

Answer 6

That is what I got.

Answer 7

okay so c = 93 seats in row 15, and part b is a(19)=(3*19)+36

Answer 8

you don't have to use the formula of an=a1+(n-1)d?

Answer 9

Part (b) is the general formula. --> b. Write the general terms for a sequence a n that gives the number of seats in row n.

I marked parts a, b, and c in one of the posts on this thread. Look about five posts up.

Answer 10

an=a1+(n-1)d

This is the general term for any term of any arithmetic sequence.

Part (b) asks for the general term formula for this particular "how many seats on a row" arithmetic sequence.

Answer 11

so our general term formula is an=3n+36

Answer 12

Looking at this one:
an=a1+(n-1)d

a sub 19 = 39 + (19 - 1)*(3)

a sub 19 = 39 + 18*3
a sub 19 = 54 + 39
a sub 19 = 93

Answer 13

In answer to your question, part b refers to "for a sequence." I assumed that by "for a sequence," that this particular sequence is the one for which the general term is asked. So, I don't know.

Answer 14

okay this is how I answered it \[a _{n}= a _{19} = 39+(19-1)3\]

Answer 15

^^^ That is the work and answer for part c.

Answer 16

The general term cannot have a "19" in it because if it does, then it is not the general term formula. It is the formula for the 19th term.

Answer 17

okay so just \[a_{n}=39+(19-1)(3)\]

Answer 18

This is my idea of a general term formula for THIS particular sequence an=3n+36 on part (b).

Again, if your general term formula shows a NINETEEN, then it is NOT general. It is a specific formula for the 19th term. That is not what part (b) is asking.

Answer 19

okay, phew I can't wait till this class is over.

Answer 20

It is a language problem that we have encountered on part b. So, it is not our fault that the language is poorly written.

I would enter an=3n+36 OR an=39 +(n-1)*3 for part (b) and vigorously defend what I wrote is correct given the vagueness of part (b). But, don't have a "19" showing because the formula is no longer the general formula for the number of seats on a row in the seat sequence 39, 42, 45, ...

Answer 21

I'm interested to know what turns out to be the "correct" answer. So, let me know, please.

Answer 22

I am going to use the or just because that is what formula we have been using or the "look" of how some of our answers.

Answer 23

it's a geometric or arithmetic type of sequence?

Answer 24

Okay.
From above in the thread, a) Okay, so the sequence appears to be arithmetic with d (common difference) of 3.

Answer 25

YOU were correct!!!

Answer 26

WE were correct. :)