Finding the value of a term

**mathfanatic** · September 16th 2008, 11:19 AM

I am stuck on a problem here that I have been looking at since last week. If someone could guide me in the right direction I would appreciate it before my head explodes!

SEE ATTACHED DOCUMENT: I did not realize when I copied and pasted the original equation it changed it to the same size font. It was an intelligible equation when I typed it.

I am utterly lost. Where would I even begin in order to solve?
Thanks for any help!

**CaptainBlack** · September 16th 2008, 11:59 AM

Originally Posted by mathfanatic

I am stuck on a problem here that I have been looking at since last week. If someone could guide me in the right direction I would appreciate it before my head explodes!

a1=3, ak+1=ak-2
What is the value of the 4th term?
I am utterly lost. Where would I even begin in order to solve?
Thanks for any help!

$a_{k+1}=a_{k-2}$

so if $k=3$ , we have: $a_4=a_1=3$

RonL

**mathfanatic** · September 16th 2008, 12:08 PM

Originally Posted by CaptainBlack

$a_{k+1}=a_{k-2}$

so if $k=3$ , we have: $a_4=a_1=3$

RonL

Did you get k=3 from the a1=3?

I am sorry, I am so lost with this!

**Opalg** · September 16th 2008, 12:14 PM

You need to write this problem more clearly to make it intelligible. It's obviously about a sequence of terms $a_1,\,a_2,\,a_3,\,a_4,\ldots$ , and you're given two equations to enable you to calculate these terms. The first equation presumably says $a_1=3$ . In other words, the first term in the sequence is 3 (and the 1 in that equation is a subscript). I'm guessing that the other equation is meant to tell you how to find $a_{k+1}$ if you know $a_k$ . In other words, the k+1 on the left-hand side is a subscript; but on the right-hand side, only the k is a subscript, not the -2. Am I right so far?

If I am, then the second equation probably says either $a_{k+1} = a_k-2$ or $a_{k+1} = a_k^{-2}$ . If it's the first of those, then it is saying that you subtract 2 from each term of the sequence to get the next term. If the -2 is meant to be a power of $a_k$ , then it's saying that you must raise each term of the sequence to the power -2 to get the next term.

Whichever of those two versions is correct (or maybe it's something else altogether?), you apply that rule to the first term $a_1$ (namely the number 3) in order to get the second term $a_2$ , and then repeat the same process to get $a_3$ and finally $a_4$ .

Edit. Another possible interpretation is the one that CaptainBlack is suggesting, namely $a_{k+1} = a_{k-2}$ , with the whole of the k-2 as a subscript. In that case, each term is equal to the one that came three terms before it (because the difference between k+1 and k-2 is 3). In that case, $a_4=a_1$ as he says.

**Soroban** · September 16th 2008, 12:47 PM

Hello, mathfanatic!

It's impossible to read what you typed,
. . but I'll take an educated guess . . .

$a_1\:=\:3,\quad a_{k+1} \:=\:a_k-2$ . . . I hope this is right!

What is the value of the 4th term?

It says (I think): . $a_{k+1} \;=\;a_k - 2$

That is, each term is two less than the preceding term.
[The sequence "goes down by 2's."]

Then: . $\boxed{\begin{array}{ccc}a_1 &=& 3 \\ a_2 &=& 1 \\ a_3 &=& \text{-}1 \\ a_4 &=& \text{-}3 \\ a_5&=& \text{-}5 \\ \vdots &&\vdots\end{array}}$

Got it?

**mathfanatic** · September 16th 2008, 12:57 PM

Thanks-yes I didn't realize when I pasted it from Word that it changed the font-I attached it as a document later.

But this is a PERFECT explanation!! You have been absolutely a wonderful help-I am so happy!!

Thank you thank you thank you!!!!! You made my day!!

Originally Posted by Soroban

Hello, mathfanatic!

It's impossible to read what you typed,
. . but I'll take an educated guess . . .

It says (I think): . $a_{k+1} \;=\;a_k - 2$

That is, each term is two less than the preceding term.
[The sequence "goes down by 2's."]

Then: . $\boxed{\begin{array}{ccc}a_1 &=& 3 \\ a_2 &=& 1 \\ a_3 &=& \text{-}1 \\ a_4 &=& \text{-}3 \\ a_5&=& \text{-}5 \\ \vdots &&\vdots\end{array}}$

Got it?

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