Question

given f(4)=-23 and f(9) = -58, for an arithmetic sequence, find the general term. help please!

Answer 1

Arithmetic Progression follows the format \[\large a_{n}=a_{1}+(n-1)d\]

Answer 2

Very true. Let's get creative. Normally we work with a1, but let's imagine a4 is the first term and a9 is an. What would n be in that case?

Answer 3

Oh? Yeah that's somewhat similar to how I solved it...

Answer 4

Once we know n, we can find d. We can get a1. We can get the general formula.

Answer 5

How far apart are a4 and a9? That amt takes the place of (n-1).

Answer 6

so in this case An would be -58?

Answer 7

Oh, i see.

Answer 8

5-1...ah.

Answer 9

Yes.

Answer 10

but why does n become 9?

Answer 11

No no, it's not 9.

Answer 12

I wish d ended up a pretty number. Hmm....

Answer 13

We have to look at what the formula really means. It says:

an = a term
a1 = a term before an
(n-1) = how far apart an and a1 are
d = how far apart consecutive terms are

Answer 14

Okay, so that means its-58= -23+(5-1)d

Answer 15

the question asks to solve for the general term but in this case we find d?

Answer 16

Not 5-1, but acutally 5. See term 4 and term 9 are 5 places apart.

Answer 17

\[\large a_{n}=a_{1}+(n-1)d\]

There taking this formula and @mrbarry 's analysis of the arithmetic progression process,

we can say that the distance between f(9) and f(4) is 5 numbers. So 5 = n.
we're given f(4) = -23 so a1 = -23
we're given up to the number we want to find up to (an) and that's represented by f(9) = -58 we're trying to reach -58.

Answer 18

@Jhannybean are you comfortable with my generalization of the formula?

Answer 19

oh gosh, i still dont understand how to solve this question

Answer 20

And yes I am @mrbarry

Answer 21

so substitution and elimination are taking place?
-23 = a + d(4-1)
-58 = a + d(9-1)

Answer 22

yup

Answer 23

@talha111 remain calm. This is one of those situations where we have to WORK our way to the solution.

To get from term 4 to term 9 there are five jumps.
To get from -23 to -58 you move -35.
Each jump is worth -35/5 = -7 (Now we have d)

We can go back to the original equation and use term 4 or term 9 for an. We know all but a1 so now we can find it.

a1 =

Answer 24

Arithmetic sequences are linear functions based on a domain of the natural numbers! You are a clever one.

Answer 25

Haha. deleted it because I didn't want to confuse her.

Answer 26

Are you with us talha? It's annoying when the teachers talk to each other instead of you.

Answer 27

Im here, its just that ive found a different way to solve the question, using elimination/substitution

Answer 28

which is what ive been doing for the past couple on minutes

Answer 29

Good stuff. What did you find?

You will need to substitute your a1 and d into a generic equation to get the answer we've sought.

Answer 30

so far i found d, which is 2.185

Answer 31

and ive just found a, which is -29.55

Answer 32

d won't be anything but an integer. Check again.

Answer 33

a1 is an integer also.

Answer 34

oh, my bad, ithink ive gotten the general term after fixing it, and thats an=1280(1/2)^n-l

Answer 35

hopefully this is correct

Answer 36

i got an interesting way of looking at the formula. if you didn't understand why (n-1) = 5 and not (9-1)

you have n which is the 9th term you want to reach

then you have n-1 which includes all the preceding terms.

n = 9
n-1 = 4

((n)- (n-1)) =(n-1) = 9 - 4 = 5

Therefore, you replace (n-1) with 5.