Posted by mysterychicken on Friday, June 7, 2013 at 3:11pm.
1. Determine the formula for the nth term of the following sequence: 6, 14, 22, 30, 38, 46, ...
I got an = 8n  2
Is that right?
2. The following statement is true by mathematical induction: (4/3)^n > n for all n > or equal to 6
True?
3. To find the 6th binomial coefficient of the expansion of (x + y)^15, find the value of 15C6
Not sure...
4. In how many ways can a 10question, truefalse exam be answered (assume that no questions are skipped)?
This really tricks me. I want to say 20 but I think there are more ways
5. In how many ways can 6 people sit in a 6passenger car?
Again, not sure...36?

Math  Steve, Friday, June 7, 2013 at 6:09pm
#1 looks ok
#2. sounds like you're guessing
To prove it, check when n=6
(4/3)^6 = 5.6
Bzzzt.
(However, it is true for n>6)
#3. That is correct.
The kth coefficient in (x+y)^n = C(n,k)
#4. You are correct in think that 20 is way too low.
There are 2 choices for every answer. So, there are 2^10=1024 ways to answer the questions.
#5. There are n! ways to arrange n things. So, there are 6! = 720 ways to seat 6 people in a line.
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