Question

A theater has 32 seats in the first row , 35 in the second row,38 in the third row
1. Write the general term for sequence a n that gives the number of seats in row n?
2. How many seats will be in row 19

Answer 1

this is an arithmetic sequence where the 1st term is 32 and the common difference is 3

so

\[a_{n} = 32 + ( n -1) \times 3\]

you can distribute and simplify

the next part of the question requires you to let n = 19. So substitute and evaluate

hope this helps

Answer 2

Campbell where does the n-1 come from?

Answer 3

I'm way confused

Answer 4

\[a_{n} = 32 + (3n)\]

that's what I thought it was. So for row 19 it would be 89?

Answer 5

Thank you very much:)

Answer 6

if you use @Saisaith solution you have 35 seats in the 1st row... so how is that correct...

(n - 1) occurs because you already have the 1st row in the equation and add 3 for the 2nd row.... so if n is the row number...you are adding to the previous...

so if you go back to my solution, distribute and then collect like terms you will find you have the correct solution no matter what row number you are looking at.

hope this helps...

Answer 7

Ah see that is why I was asking where you got the n-1 from which makes sense now that I actually think about it.

Thanks campbell!

Answer 8

So do I substitute 19 in 32+(19-1)*3

Answer 9

I'm still lost sorry

Answer 10

well thats the solution for the 19th row

the general solution is

\[a_{n} = 32 + 3n - 3\]

can you simplify this equation..?

Answer 11

Combine 32-3 =29/3=n?

Answer 12

not quite try

\[a_{n} = 3n + 29\]

and you may notice now... n = 1 the number of seats = 32...
n = 2 the number of seats = 35

so it seems to work

Answer 13

so to find the 19th row

\[a_{19} = 3 \times 19 + 29\]

hope this helps...

Answer 14

86 seats ?