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!
You need to write this problem more clearly to make it intelligible. It's obviously about a sequence of terms , and you're given two equations to enable you to calculate these terms. The first equation presumably says . 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 if you know . 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 or . 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 , 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 (namely the number 3) in order to get the second term , and then repeat the same process to get and finally .
Edit. Another possible interpretation is the one that CaptainBlack is suggesting, namely , 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, as he says.
It's impossible to read what you typed,
. . but I'll take an educated guess . . .
. . . I hope this is right!
What is the value of the 4th term?
It says (I think): .
That is, each term is two less than the preceding term.
[The sequence "goes down by 2's."]