- How do I find explicit definitions with a few terms in a sequence? When do I have to use a definition to prove a sequence?
- I will probably make mistakes when creating a definition and with the fibonacci's sequence since I don't feel I fully understand it.
- 4.9, -0.9, -5.7...
- Say what type of sequence it is.
- Find the difference or the ratio (d or r).
- Create a formula.
- Find the 11th term.
5 comments:
- It is an Arithmetic Sequence.
- d= -5.3
- Tn= t1+ (n-1)(d)
T11= 4.9 + (11-1)(-5.3)
- 11th term= -48.1
Bee,
Do you want your 3rd term to be -6.7?
If the 3rd term is -6.7 insted of -5.7 then yes it is an arithmetic sequence.The difference is not -5.3, -.9-4.9 = -5.8
Therefore, the equation would be:
T11 = 4.9 + (11-1)(-5.8)
T11 = 4.9 - 58
T11 = -53.1
To prove a sequence just with a definition, you have to be given a limited amount of numbers rather than a sequence that goes on forever. Sequences that go on forever will have three dots after a few numbers (...).
When you have such sequence then you will have to give an equation along with the definition.
The definition you give as a proof is the one that belongs to the kind of sequence you are trying to prove it is.
Example 1:
given: {-2.5, -1.5, -0.5, 0.5, 1.5, 2.5}
Proof:
This is an Arithmetic sequence because the diffrence between any two consecutive terms is a constant (x+1). ex: -2.5+1=-1.5
So, if you are given a sequence like {2, 4, 8, 16,...)
then you should give a definition
ex: This is a geometric sequence because the ratio between any two consecutive terms is a constant.(x*2)
Then, you would have to give a formula which fits that definition and will allow you to figure out the nth term in the sequence.
ex: term n= 2*(2^n-1)
so for term7= 2*(2^6)
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