91Ó°ÊÓ

a. Tell whether the sequence is arithmetic, geometric, or neither. b. Write the next two terms. c. Find \(t_{100}\) d. Find the term number of the term after the first ellipsis marks. $$0,3,8,15,24,35,48,63,80,99, \ldots, 3248, \ldots$$

Piggy Bank Problem: Suppose that you decide to save money by putting \(\$ 5\) into a piggy bank the first week, \(\$ 7\) the second week, \(\$ 9\) the third week, and so forth. a. What kind of sequence do the deposits form? How much will you deposit at the end of the tenth week? In what week will you deposit \(\$ 99 ?\) b. Find the total you would have in the bank at the end of the tenth week. Show that you can calculate this total by averaging the first and the tenth deposits and then multiplying this average by the number of weeks. c. What is the total amount you would have in the bank at the end of a year? (Do the computation in a time-efficient way.)

Factorial Sequence Problem: These numbers form the sequence of factorials: $$1,2,6,24,120,720, \dots$$ a. Figure out a recursive pattern in the sequence and use it to write the next two factorials. b. Recall from Chapter 9 that you use the exclamation mark, \(1,\) to designate a factorial. For example, \(6 !=720 .\) Write a recursion formula and use it to find \(10 !\) and \(20 !\). What do you notice about the magnitude of the values? Think of a possible reason the exclamation mark is used for factorials.

Expand as a binomial series and simplify. $$(x-y)^{3}$$

Expand as a binomial series and simplify. $$\left(x^{2}+y^{3}\right)^{6}$$

Find the indicated term in the binomial series. $$\left(x^{3}-y^{2}\right)^{13}, x^{18} \text { -term }$$