Question

A theater has has 47 seats in the first row 51 seats in the second row, 55 seats in the third row and so on?
(a) can the number of seats in each row be modeled by an arithmetic or geometic sequence?
(b) Write the general term for the sequence an that gives the number of seats in row n
(c ) How many seats are in row 19?

Answer 1

What do you do to get the number of seats in each successive row?

Answer 2

This is an arithmetic sequence. See, 47+4 = 51, 51+5 = 55. See?

Answer 3

It would be great if the asker were allowed to make these discoveries.

Answer 4

Now consider, the first row with 47 seats is A1 (meaning the first term)

Answer 5

Hey, I take online courses and its hard learning all this stuff just reading a text book. I am a visual learner and just would like help on explaining. thanks.

Answer 6

If the first term is 47, then the 2nd term is 51. How did I get this? I added one. So A2 is 4 + A1. A3 is 54, which is A1 + (2*4)
Thus, the formula is A1+4n starting from n=0 to n = infinity

47 + 4n

Answer 7

The 19th row is A19.

An = 47 + 4n
A19 = 47 + 4(19) = 123 seats.

I hope this helped! I hope to help you in the future, I am new to this website.

Answer 8

This is great! I have a final next Sunday and writing this all down for my notes!

Answer 9

so an=4?

Answer 10

No problem! The trick to know that something is arithmetic is to understand how each successive (next term) is changing. A general rule you should try always is subtract successive terms. Like A2 - A1, A3 - A2, A4 - A3... If all of these are the same (51-47 = 5, 55-51 =4) then it is arithmetic.

Answer 11

An means A sub n. This mean the nth term in the sequence.

Answer 12

The general formula for arithmetic sequence (notation may vary) is:

An = A1 + Dn
A1 is the 1st term, starting term in this case is 47.
D is the common difference, or in this case +4 seats per row.
n is the nth term, or in this case part c the n = 19

Answer 13

ok so when it says write the general term for the sequence an that gives the number of seats in row n ?

Answer 14

That question part b is asking to give "An = A1 + Dn". It's saying "give me the function for which I plug in a value n, and I get the value of term n"

Answer 15

A19 = 47 + 4(19)

Answer 16

correct. For example, if I asked for A25, that means the 25th row, it would be:
A25 = 47 + 4(25) = 147 seats in row 25

Answer 17

ok I see

Answer 18

Most questions will be in this format. First they will ask you whether the system is arithmetic or geometric - and why. Then they will ask for the general term, otherwise known as the function. Then they will ask you to apply it, by finding some term n by plugging in n into the function

Answer 19

ok thank you :)

Answer 20

No problem, and good luck!