Question

how do I find the general term \[a{n}\] for the geometric sequence \[a{1}= -4 and a{2} = 12

Answer 1

well at first you need to find the rate that the sequence goes, in this case can you find it?

Answer 2

no, i have no idea.

Answer 3

Ok, the rate is the number that when it multiplies a1 it gives a2, when it multiplies a2 it gives a3, and so on, thats the definition of geometric sequence, now try again, remember: a1*rate=a2

Answer 4

Im sorry, I really do not understand....I dont even know how to start it???

Answer 5

so how does -4 and 12????

Answer 6

I dont get it

Answer 7

Ok, do you know what a sequence is? If yes, do you know what a geometric sequence is?

Answer 8

not really....I know what a sequence is and how to find it with common numbers.

Answer 9

so the next number would be 28???

Answer 10

i dont understand what the general term is??

Answer 11

Not 28, lets begin from the begining. A geometric sequence is a sequence of numbers where they are multiplied again and again to find the next always by the same number. Like that: 3, 6, 12, 24, 48, ... In this case, the number wich is multiplying is 2 and it is the rate at wich the numbers are evolving. The general term, is any term that belongs to the sequence, for example in this sequence I showed above, the 10th term can be found by multiplying the first one 9 times by 2, and what the exercise wants is the formula that gives this term without you having to do every multiplication. How is it going so far?

Answer 12

28 would be an arithmetic sequence, where you sum the same number over and over, not multiply.

Answer 13

thats what I do not know how to find??? -4, 12 and this a(n) I dont get it? a(1) a(2)

Answer 14

so would it be 16?

Answer 15

No, lets make a list, I think it will help:
a1*r=a2
a2*r=a3
a3*r=a4
.
.
.
\[a_{n-1}*r=a_{n}\]
Thats a geometric sequence and an is the general term.
When its writen like that, you need to multiply over and over. What you want in this problem is to find one single formula, do you prefer to do it without numbers first and put the numbers in the end or the opposite? In both ways you will eventually need to find r so try to find it now.

Answer 16

so i just make that list till i get to the numbers but which one is the general term????

Answer 17

i have no idea....so lost

Answer 18

lets try numbers at the end

Answer 19

Ok, sorry for letting you wait. The general term is not a specific term, its a formula that gives you the term that you want, if you want the 10th term, you use the formula, if you want the 123313th term, you just use the formula, thats why its general.

Answer 20

Lets begin by using a finite number in a general sequence.
a1*r=a2
a2*r=a3
a3*r=a4
Now try to find a5 but as a function of a1.

Answer 21

I am so sorry, I jsut do not understand what to do?? I dont no what a5 means as a function of a1????

Answer 22

Its ok, ill explain it.
First continue the list above to find a5.

Answer 23

a3*r=a5

Answer 24

Almost, it would be a4, do you se why?

Answer 25

Instead of a3

Answer 26

no

Answer 27

oh shoot, i see that

Answer 28

Ok, now looking at the list you get a4=a3*r.
And acording to you we get a5=a4*r.
But since you know what a4 is, you can put it on the formula for a5.
What do you ger?

Answer 29

so a5 = a4*a3?

Answer 30

No, put a4=a3*r in a5=a4*r, and you should get a5=a4*r=(a3*r)*r=a3*r^2.
Do you understand that?

Answer 31

oh my gosh,no. it is like reading greek. im sorry, i just do not understand.

Answer 32

Its ok, you'll get it.
a4=a3*r, so far so good.
a5=a4*r, in the place of a4, you just put a3*r, wich you already know from above, that is the same thing as a4.
Is it better?

Answer 33

a little, I still dont understand how I use -4 and 12??? :)

Answer 34

Don't think about this, just focus on finding the general term, thats what we are doing first withou numbers.

Answer 35

ok

Answer 36

Now look two posts above, and try to understand why a5=a3*r^2

Answer 37

3 posts

Answer 38

because a4 is the same as a3*r^2

Answer 39

almost I think you read it wrong again, but you understood, its r not r^2.
Now do the same thing for a3, substitute it for a2*r, that we found on the list.

Answer 40

Are you still here?

Answer 41

yes, sorry

Answer 42

Take your time, not a problem.

Answer 43

a5=a2*r

Answer 44

You forgot some r in the way, try to find it.

Answer 45

a5=(a2*r)*r

Answer 46

almost again, the problem is still the r, it was squared when we were using a3, now with a2, its (a2*r)*r*r, try to see it, and then substitute a2 by a1*r

Answer 47

ty for all your help, but I just dont get it...I give up for today. ty again.

Answer 48

You are almost there are you sure you want to leave now?
If you want I can give you the answer for you to try again later.

Answer 49

ok, if you would like, that would help. then i can go over it again and again