Math

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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 10-question, true-false 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 6-passenger car?
Again, not sure...36?

  • Math -

    #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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