1. How do you write a recursive definition (especially for a geometric sequence)?
Also, question #41 in the homework sais "How many 3-digit numbers are divisible by 4 and 6?
I'm not sure if that kind of question is going to appear in the quiz but, if it is, I have no idea how to solve for that one. How do you solve this problem?
2. I will most likely get some answers wrong on the quiz by getting mixed up when I'm plugging in numbers in the formulas for each sequence. Also, writing recursive definitions give me a bit of a problem because I keep forgetting how to do them (Maybe I'll have to pay a bit more attention to the forgetting curve).
3. For the sequence {4, 9.2, 14.4, 19.6 ...}
a) Determine if it is geometric, arithmetic or neither.
b) Give an explicit definition for it.
c) Find the 10th term.
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4 comments:
a)Arithmetic
b)t(n)= 5.2n-1.2
c)50.8
Add: How to give a recursive definition if it is not an arithmetic or geometric sequence?
Answer to question 44: How many 3-digit numbers are divisible by 4 and 6?
3-digit numbers go from 100 to 999.
The least common multiple of 4 and 6 is 12, so we have to find how many numbers between 100 and 999 are divisible by 12.
Term(1) would be the first number, begginning at 100, that is divisible by 12, that number is 108, because 12*9=108.
The last term would be the last number before 999 that is divisible by 12. That number is 996, because 12*83=996.
To find out which term is 996 we can apply the explicit definition and solve for the number of the term.
t(n)=t(1)+(n-1)*d
t(n)=108+(n-1)*12=996
(n-1)*12=996-108
12n-12=888
12n=900
n=75
There are 75 3-digit numbers divisible by 4 and 6.
Check the answer...
Mac, I would have never thought of solving that problem that way. But I was having that same problem when doing the homework... and your way works. !!
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