Assignment: Read the following problem and its solution. ANSWER THE QUESTIONS THAT FOLLOW IN COMPLETE SENTENCES AND PROVIDE THE CORRECT UNITS WHEREVER NECESSARY. EQUATIONS ARE NOT REQUIRED. There are 120 passengers in the rst carriage, 125 passengers in the second carriage, 130 passengers in the third carriage, and so on (the number of passengers form an arithmetic sequence). What is the number of passengers in the ninth carriages? Solution: To recall, the sequence ((1n)"E N such that each term is obtained from the preceding one by adding a constant is an arithmetic sequence. That means that any arithmetic sequence has a form a,a+d,a+ 2d,a+ 3d,a+ 4d,... where the constant d is called the common difference. The formula for the n-th term of an arithmetic sequence is a=a1+(n1)d Numbers of passengers in carriages are the arithmetic sequence a with the initial element (11 = 125 and the difference d = 5. For this reason, it is (19 = a1 + (9 1)d = 125 + 8 X 5 = 165 Now answer the following question(s). 1. What are the different types of Sequences? 2. What is the type of Sequence that applies to the number of passengers in the Carriages? 3. Dene Arithmetic Sequence. 4. Dene: a. Recursive formula (using words. Formulas and examples are not required.) b. Explicit formula (using words. Formulas and examples are not required.) 5. In an arithmetic sequence a,a+d,a+ 2d,a+3d,a+4d,... a. What is (1 called? b. What is dcalled