# Thread: Finding the value of a term

1. ## Finding the value of a term

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!

2. 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!
$\displaystyle a_{k+1}=a_{k-2}$

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

RonL

3. Originally Posted by CaptainBlack
$\displaystyle a_{k+1}=a_{k-2}$

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

RonL

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

I am sorry, I am so lost with this!

4. You need to write this problem more clearly to make it intelligible. It's obviously about a sequence of terms $\displaystyle a_1,\,a_2,\,a_3,\,a_4,\ldots$, and you're given two equations to enable you to calculate these terms. The first equation presumably says $\displaystyle a_1=3$. 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 $\displaystyle a_{k+1}$ if you know $\displaystyle a_k$. 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 $\displaystyle a_{k+1} = a_k-2$ or $\displaystyle a_{k+1} = a_k^{-2}$. 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 $\displaystyle a_k$, 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 $\displaystyle a_1$ (namely the number 3) in order to get the second term $\displaystyle a_2$, and then repeat the same process to get $\displaystyle a_3$ and finally $\displaystyle a_4$.

Edit. Another possible interpretation is the one that CaptainBlack is suggesting, namely $\displaystyle a_{k+1} = a_{k-2}$, 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, $\displaystyle a_4=a_1$ as he says.

5. Hello, mathfanatic!

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

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

What is the value of the 4th term?

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

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

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

Got it?

6. ## Thank you!!

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): .$\displaystyle a_{k+1} \;=\;a_k - 2$

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

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

Got it?