H2O wrote:Can someone please tell me how to understand this problem. I think the reason I don't know how to approach it is because I'm not sure what the question is asking.
In the arithmetic sequence T1, T2, T3,...Tn...T1=23 and Tn=Tn-1=-3 for n>1. Wht is the value of n when tn=-4?
1. -1
2. 7
3. 10 correct
4.14
5.20
Many thanks!
i presume the formula is supposed to say something like
Tn = Tn-1 - 3
?
you have an extra equals sign in there, and that really messes with the formula.
this is an example of a RECURSIVE SEQUENCE; you should learn to interpret such formulas conceptually. in these formulas, just think of "Tn" (or "An" or "whatever else sub n") as
the current term, and "Tn-1" (or An-1 or whatever) as
the previous term. try using these conceptual interpretations, rather than trying to plug in literal numbers, and it should be easier for you to interpret the formulas.
...so if you see something like
Tn = Tn-1 - 3
then you interpret it as
the current term is the previous term minus three
which means that you're just subtracting 3 every term.
you can use formulas, as the previous poster has done; if you're not much for memorizing formulas, then you can do one of the following 2 things:
(1)
find the number of "steps" between the two values: the two values in this case are 23 and -4. the difference between those two values is 27, which is nine "steps" (since 3 is subtracted each time). since you started with the first term, nine "steps" later is the tenth term.
btw, this is essentially what that formula does, but it's better because you aren't held hostage by the first term: in other words, if 23 were the nineteenth term, then -4 would be the 19 + 9 = 28th term.
(2)
just grind the sequence until you reach the desired term: since the answer choices are all relatively small numbers, you know that you can just find terms of the sequence until you get -4 as one of them:
23 20 17 14 11 8 5 2 -1 -4
looks like -4 is the tenth term.
this method is probably the fastest one for this problem, although it has obvious limitations that will come to light if you try to use it for a sequence that has hundreds or thousands of terms.
