Question

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?

Answer 1

#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.