Download Chapter 11

Chapter 11 Review Problems:
1. Expand (3x  2) 6 . (use the Binomial Theorem or Pascal’s triangle)
2. Use Mathematical Induction to show that the given statement is true for all natural numbers.
3  6  12  ...  3  2 n1  3(2 n  1)
3. Find the nth term ( a n ) of the following arithmetic sequence:
a7  31 and a20  96
4. Determine whether the infinite geometric series converges or diverges. If it converges, find its
sum.
8 16
6  4    ...
3 9
5. Write the following number is fraction in lowest term.
2.37  2.3777777...
38
6. Find the sum.
 (3k  9)
k 5
7. Find the 12th term in the expansion of ( x  3 y)15
8. Find the nth term ( a n ) of the following geometric sequence:
1
1
a 4  and a9  
4
128
9. You are offered a 6-week summer job and are asked to select one of the following salary options:
Option 1: $5000 for the first day with a $10,000 raise each day for the remaining 29 days.
Option 2: 1 cents for the first day with the pay doubled each day.
Calculate your salary for each option.
10. For many years, the state of California used 3 letter followed by 3 digits on its automobile
license plates:
a. How many different license plates are possible with this arrangement?
b. When the state ran out of new numbers, the order was reversed to 3 digits followed by 3
letters. How many new license plate numbers were then possible?
c. Several years ago, the number also used up. The state then issued plates with 1 letter
followed by 3 digits and then 3 letters. How many new license plate numbers will this
provide?
11. A legislative committee consists of 6 Republicans and 4 Democrats. A delegation of 3 is to be
selected to visit Iran.
a. How many different delegations are possible?
b. How many delegations would have all Republicans?
c. How many delegations would have 2 Republicans and 1 Democrat?
d. How many delegations would include at least 1 Democrat?
12. From a cooler with 8 cans of a different kinds of soda, 3 are selected from 3 people. In how
many ways can this be done?