Question

Initially, a store has 35 train sets. The store sells 3 train sets each month.

What is a explicit rule for the number of train sets the store has after n months?
An=?

Answer 1

this is an arithmetic sequence
a1 (first term) = 35
d (common difference) = -3

Answer 2

So what will that mean?

Answer 3

an = a1 + d(n - 1)

Answer 4

Oh.

Answer 5

- well just plug those values into the general formula (in my last post)

Answer 6

Okay

Answer 7

Note how welshfella has come up with an equation that enables you to calculate how many train sets are still available after n months?

What is the initial value of that function?
What is the common difference?

welshfella knows what he's doing.

Pls share your work.

Answer 8

\[nth ~term ~ is ~a _{n}\]

Answer 9

So what I come up with will be the answer

Answer 10

\[First ~ is ~a _{1}\]

Answer 11

common difference, d, is what?
What does n represent?

Answer 12

d(n-1)?

Answer 13

as welshfella has said, plug in the knowns to obtain a formula.

d(n-1) is part of your formula. What's the whole formula? The purpose of this formula is to calculate the nth term of your sequence.

Answer 14

Well I'm very familiar of how to finish it tbh

Answer 15

That statement seems to say, "I'm sure I can finish it." Is that what you meant to say?

Answer 16

No, I'm not sure how to finish it, sorry

Answer 17

From welshfella: an = a1 + d(n - 1)

where the first term is 35, the common diff is d, the index of the answer you want is n,
and an is the nth term.

Start substituting these knowns (first term and common difference) into the equation.

Answer 18

Ahh okay

Answer 19

3(n-35)?

Answer 20

Please type out the entire formula.

Start it with \[a _{n}=\]

Answer 21

Next, write in the value of the first term (35).

Answer 22

Next, write in d(n-1), but before you do that, replace "d" with the "common difference."

Answer 23

The common difference is 35, right?

Answer 24

\[a _{n}=35+????\]

Answer 25

No, the first term is 35. The store starts out with 35 train sets in stock and sells 3 sets each month. What is the common difference? Is the # of train sets increasing or decreasing?

Answer 26

Well it seems to be decreasing when they sell 3 sets each month

Answer 27

If increasing, then the common diff is +, but if decreasing, then the com. diff. is - .

Answer 28

So, what is the common difference?

Answer 29

d=?

Answer 30

3?

Answer 31

Is the # of train sets in stock in the store incr or decr?

Answer 32

Its decreasing

Answer 33

Then the common diff must be negative.

What is the common diff?

Answer 34

Oh, so must I subtract 35 and 3?

Answer 35

No. You begin with \[a _{n}=35+d(n-1)\] and replace "d" with "-3." Do that now, please. Keep in mind what these numbers stand for.

35 is the starting count of the number of sets on hand.
-3 is the common difference, d.
n is the count: 1, 2, 3, and so on.

Answer 36

Oh, I'm sorry for giving a hard time, sorry

Answer 37

You're learning, so I'm happy.

Answer 38

So how would I write that equation?

Answer 39

\[a _{n}=35+(-3)(n-1)\]

Answer 40

Please simplify: " +(-3) "

Answer 41

(+)(-)=?

Answer 42

lol I have no clue of how to simplify

Answer 43

(+)(-)=(-)

So you end up with \[a _{n}=35-3(n-1).\]

Answer 44

This is the answer you wanted. Please, review this entire discussion and ask any necessary questions that might help you arrive at a complete understanding.

Answer 45

Ahh okay I get it now

Answer 46

I wrote it all down in notes

Answer 47

This formula is "arithmetic sequence," that is, a formula for the nth term of an arith sequence when the starting value (a_1), the common diff (d) are known.
n is just a counter: it begins with 1, moves on to 2, 3, 4, .... and so on.

Answer 48

Okay, I'll write that down, the post another subject, one sec..

Answer 49

\[a _{n}=?\]

Answer 50

can you now define what that means?

Answer 51

As for this problem?

Answer 52

Yes. What does that a_n represent? answer in words only.

Answer 53

It represents N=1

Answer 54

It represents "the nth term of an arithmetic sequence."

Answer 55

a_1 is the first term, a_2 is the second term, and so on.

what does "d" stand for?

Answer 56

From what I wrote, D stands for the Difference, am I right?

Answer 57

common difference. Yes.

Answer 58

What does "n" stand for?

Answer 59

Oh, common difference lol sorry

Answer 60

N is the number count for 1,2,3,4,5, and so forth

Answer 61

Yes. we call it an "index." for example, I might say, "Hey, Nerd, give me the 4th member of this arith sequence." n would be 4.

What does a_1 stand for?

Answer 62

It represents the first term of the Arithmetic sequence

Answer 63

Right. And in this particular problem (case), what is the value of a_1?

Answer 64

3?

Answer 65

Again, what does a_1 represent? '3' is something else.

Answer 66

You could, of course, go back and review this discussion if necessary, to review what a_1 represents.

Answer 67

Yes I just did, it represents one, right? I don't believe I wrote that down in my notes

Answer 68

a_1 is the starting value of this arith sequence, and is 35.

Answer 69

Which is the first term

Answer 70

Yes, it's the first term.

Answer 71

Oh

Answer 72

I'm gonna write that down right now

Answer 73

\[a _{n}=a _{1}-3(n-1)\]

Answer 74

is the answer to this particular question. Hey, Nerd, what's the 7th term of this sequence?

Answer 75

Let n=7 in this formula\[a _{n}=a _{1}-3(n-1)\]

Answer 76

Ah okay

Answer 77

7-1=?

Answer 78

6

Answer 79

Shall I post my next problem?

Answer 80

Let's go thru that: a_7 = 35 - 3(6), or 35-? = ?

Answer 81

Therefore, a_7 = ??

Answer 82

a_7 = 35 - ??

Answer 83

a_7=35

Answer 84

3(6)

Answer 85

but -3(6) = -18.

So, a_7 = 35 - 18 = ??

Answer 86

35
-18
------
?

Answer 87

17

Answer 88

yes, and so a_7 = 35 - 17 = ?

Answer 89

18

Answer 90

a_7 represents the number of remaining train sets after 7 weeks of sales of the trains.

Answer 91

Yes. The store has 18 sets left after 7 weeks. Yes.

Answer 92

That makes better sence lol

Answer 93

Formulas, formulas. gotta learn to be comfy with them.

Answer 94

algebraic representation, algebraic rep, gotta be comfy.

Answer 95

Well its a little difficult cuz I hate Math XD

Answer 96

Come on, you like math and you're liking it better day by day. ;)

Answer 97

Altho' I cannot help you with your remaining questions right now, I'll be back on sev eral times later today. You could either post your next question now and wait for another helper to respond, or you could look for me on OpenStudy later in the day.

Answer 98

lol okay, thank you so much