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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 n1 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?