91Ó°ÊÓ

DIFFERENT WORDS, SAME QUESTION Which is different? Find "both" answers. What sequence consists of all the positive odd numbers? What sequence starts with 1 and has a common difference of 2 ? What sequence has an \(n\)th term of \(a_n=1+(n-1) 2\) ? What sequence has an \(n\)th term of \(a_n=2 n+1\) ?

How can you determine whether a sequence is geometric from its graph?

Consider the infinite geometric series. Find and graph the partial sums \(S_n\) for \(n=1,2,3,4\), and 5 . Then describe what happens to \(S_n\) as \(n\) increases. $$ \frac{1}{2}+\frac{1}{6}+\frac{1}{18}+\frac{1}{54}+\frac{1}{162}+\cdots $$

tell whether the sequence is arithmetic. Explain your reasoning. \(36,18,9, \frac{9}{2}, \frac{9}{4}, \ldots\)

In Exercises 5–12, tell whether the sequence is geometric. Explain your reasoning. \(5,20,35,50,65, \ldots\)

In Exercises 5–12, tell whether the sequence is geometric. Explain your reasoning. \(0.3,-1.5,7.5,-37.5,187.5, \ldots\)

Write a rule for the arithmetic sequence with the given description. a. The fi rst term is ?3 and each term is 6 less than the previous term. b. The fi rst term is 7 and each term is 5 more than the previous term.

Write a recursive rule for the sequence. $$ 54,43,32,21,10, \ldots $$

Write a rule for the geometric sequence with the given description. a. The first term is \(-3\), and each term is 5 times the previous term. b. The first term is 72 , and each term is \(\frac{1}{3}\) times the previous term.

Compare the terms of a geometric sequence when \(r>1\) to when \(0