Question

Find the first six terms of the sequence.

a1 = -8, an = 5 • an-1

Answer 1

Explanation please!

Answer 2

Hello, Tonio,
Looks like the first term of your sequence is -8 (which you have called "a1").
The nth term is 5*a(n-1) (which you have called an-1).
Let me type that in Equation editor:\[a _{1}=-8;a _{n}=5*a _{n-1}\]

Answer 3

So, if the first term, a1=-8, the second term is \[a _{2}=5a _{2-1}=5a _{1}=5(-8)=-40\]

Answer 4

Please look that over. Then see whether you can find the third, fourth, fifth and 6th terms. Please write out your work (here, or on paper and then share the image with me).

Answer 5

oh okay so
\[a _{3}=5a _{3-2}=5_{a2}=5(-40)=-200\]?

Answer 6

@mathmale

Answer 7

Looks good. Continue until you have a total of 6 terms.

Answer 8

so the terms are -8;-40;-1,000;-50,000;-250,000

Answer 9

5000 , 25000 sorry

Answer 10

Tonio: what's 5(-40)?

Answer 11

You're on the right track, but have a few corrections to make.

Answer 12

oh I forgot -200

Answer 13

I have it on my paper lol oops

Answer 14

Are you satisfied that you understand what to do, or would you like more discussion?

Answer 15

I understand some of it, let me find another equation really quick.

Answer 16

OK

Answer 17

Find an equation for the nth term of the arithmetic sequence.

-3, -5, -7, -9, ...

Answer 18

@mathmale

Answer 19

How do you get -5 from -3?
Then: how to you get -7 from -5?
Try to figure out what happens to produce a new term from the preceding term.

Answer 20

well you minus 2

Answer 21

Yes, you subtract 2 from one term to obtain the next.

Answer 22

\[a _{n+1}=a _{n}-2\]
Try testing this formula. Does it correctly predict each new a(n) value?

Answer 23

so \[a _{n}=-3+-2(n) \]

Answer 24

Best answer I could give you at this point is to ask you to do the same thing: Test whether or not your result (formula) correctly predicts each new term.

Answer 25

okay so your saying to plug in numbers?

Answer 26

when you say \[a _{n+1}\]
does this mean to add the last answer you just had or insert the answer just got?

Answer 27

Look at the sequence you've given me: -3, -5, -7, -9, ...

What is a1? what is a2? How do we get a2 from a1?

Test your own formula: try predicting a2 when a1--3. Either your formula works or it does not. Simiilarly, try testing my formula; again, either it works or it does not
In this manner you can determine the correct predictive / recursive formula.

Answer 28

when you say
an+1

does this mean to add the last answer you just had or insert the answer just got?

\[a _{n+1}\]
represents the next term in the sequence when you start with term
\[a _{n}\]

Answer 29

well I already know my formula does not work.

Answer 30

In this case your first term, a1, is -3, and your n=1.
You want to find the 2nd term, a2, from a1.

Answer 31

But in deciding that, you learned something of value, right?
It's very important to know how to check a recursive formula, as well as to actually do it!

Answer 32

yeah learing something I hate online school teachers do not help at all, but the only equation that would fit in this an=-3-2

Answer 33

learning*

Answer 34

So, where are we now? Do we have a recursion formula that "works"?

Answer 35

well it will work, but does the equation supposed have a n in it?

Answer 36

Yes, it does, but the n is a subscript, not a multiplier.

Answer 37

\[a _{n+1}=a _{n}-2\]
Your first term is a1=-3. Please predict a2.

Answer 38

a1-2=-3-2=??

Answer 39

Okay so it would equal -5

Answer 40

here let me show you my answer

Answer 41

Is that what you'd hoped for, or not?

Answer 42

an = -3 - 2

an = -3 + -2(n)

an = -3 + -2(n + 1)

an = -3 + -2(n - 1)

Answer 43

yeah but none of these look like your equation

Answer 44

(Thinking)

Answer 45

I was thinking C but not really

Answer 46

Again, I believe you'd learn the most by actually substituting n=1,2,3,4, etc., in the recursion equation (C).

Does the equation correctly predict a(n) in each case n=1,2,3, 4, etc.??

Answer 47

It appears that there may be more than 1 correct answer to this problem; one from the list given to you , one from the recursion formulas that you and I created.

Answer 48

yeah that is why I am so confused

Answer 49

Too bad you apparently MUST choose one of the four options given; that squelches creativity in finding other possible approaches.

Answer 50

Don't be offended, but I'm going to ask you to go back and double check to ensure that you
ve copied the four answer options correctly.

Answer 51

ok

Answer 52

Checking??

While waiting, I've reviewed the problem and have come up with a recursion formula that seems to work as it's supposed to:

Answer 53

\[a _{n}=-3-2(n-1)\]

Answer 54

I'd suggest you check it.
I see you're viewing someone else's question. do let me know when you're back if you'd still like to finish up the work on your own question.