Question

I need help with part B of this word problem

A theater has 46 seats in the first row, 50 seats in the second row, 54 seats in the third row and so on.
a) Can the number of seats in each row be modeled by an arithmetic or geometric sequence.
b) Write the general term for the sequence a.n that gives the number of seats in row n.
c) How many seats are in row 20?

Answer 1

@some_someone

Answer 2

46, 50, 54, ...
It would be an Arithmetic Sequence.

Answer 3

I know that this is an arithmetic sequence and that there are 122 seats in row 20 but I need help with B

Answer 4

Do you know the common difference, d?

Answer 5

Common difference is 4

Answer 6

d = 54 - 50 = 4
d = 50 - 46 = 4

Answer 7

Yes, good.

Answer 8

Now use the formula:
\[a _{n} = a _{1} = (n - 1)d\]
where:
\[a_{1}\] is the first term.
and d is the common difference.

Answer 9

Last night, another Asker and I worked this problem with different numbers. Part B is where we snagged up. I am posting the link in the event you want to look at what we did.

Again, the numbers are different but the concepts are the same.

http://openstudy.com/users/directrix#/updates/5160c868e4b06dc163b9aa03

Answer 10

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

Answer 11

its ^ that i messed up on the "+" sorry

Answer 12

\[a _{n} = 46 + (n -1)4\]

Answer 13

\[a _{n} = a _{1} + (n - 1)d\]
\[a _{n} = 46 + (n - 1)4\]
\[a _{n} = 46 + 4n - 4 \]
\[a _{n} = 4n + 42\]

Answer 14

I was correct on part c right? there are 122 seats in row 20

Answer 15

ok wait up :)

Answer 16

\[a _{n} = a _{1} + (n - 1)d\]
\[a _{20} = a _{1} + (n - 1)d\]
\[a _{20} = 46 + (20 - 1)4\]
\[a _{20} = 46 + (19)4\]
\[a _{20} = 46 + 76\]
\[a _{20} = 122\]

Answer 17

yes you were :)

Answer 18

thank you!

Answer 19

Your Welcome :)

Answer 20

Can you help me with this?

\[\sum_{k= 1}^{4}(k + 2)^2\]

Answer 21

@some_someone

Answer 22

What is the question?

Answer 23

I put the equation above ^^^^

Answer 24

Yeah but what do you want to find? The sum?

Answer 25

Sorry, Write the terms of the series and find their sum

Answer 26

First, I need to ask you what you think it is?

Answer 27

I dont know to be honest. I havent had a lot of practice with this.

Answer 28

There is two ways to approach this.
1.) To use the properties.
2.) use some simple math

Answer 29

So you know that k is the staring number, thus it says that k = 1

Answer 30

and 4 is n, thus the stopping number.

Answer 31

So it is the sum of \[( k + 2)^2\] from 1 to 4.

Answer 32

so we just plug in any number between 1 & 4?

Answer 33

So when k = 1
\[(1+2)^2\]
\[(3)^2\]
\[9\]

Answer 34

so when k = 2
\[(k+2)^2\]
\[(2+2)^2\]
\[(4)^2\]
\[16\]

Answer 35

so when k = 3
\[(k+2)^2\]
\[(3+2)^2\]
\[(5)^2\]
\[25\]

Answer 36

So when it asks what the terms of the series are: it is k = 1, n = 4?
And the sum is 9, 16, 25, 36

Answer 37

so when k = 4
\[(4+2)^2\]
\[(6)^2\]
\[36\]

Answer 38

So the sum is:
9 + 16 + 25 + 36 = 86

Answer 39

oh yea right, sum, so we need to add them.

Answer 40

yes.

Answer 41

Are you good with it?

Answer 42

You could also have used the properties and formulas.

Answer 43

yes I am, thank you