91Ó°ÊÓ

a. Show that a linear function whose domain is the set of positive integers is an arithmetic sequence. b. For the linear function \(y=m x+b, y=a_{n}\) and \(x=n .\) Express \(a_{1}\) and \(d\) of the arithmetic sequence in terms of \(m\) and \(b\) .

In \(19-30 :\) a. Write an algebraic expression that represents \(a_{n}\) for each sequence. b. Find the ninth term of each sequence. $$ 3,9,27,81, \dots $$

In \(19-24 :\) a. Write each arithmetic series as the sum of terms. b. Find the sum. $$ \sum_{i=0}^{19}(100-5 i) $$

Leslie noticed that the daily number of e-mail messages she received over the course of two months form an arithmetic sequence. If she received 13 messages on day 3 and 64 messages on day \(20 :\) a. How many messages did Leslie receive on day 12\(?\) b. How many messages will Leslie receive on day 50\(?\)

In \(19-24 :\) a. Write each arithmetic series as the sum of terms. b. Find the sum. $$ \sum_{n=1}^{25}-2 n $$

In \(19-30 :\) a. Write an algebraic expression that represents \(a_{n}\) for each sequence. b. Find the ninth term of each sequence. $$ 12,6,3,1.5, \dots $$

In \(15-26,\) write each series in sigma notation. $$ -\frac{1}{3}+\frac{2}{9}-\frac{3}{27}+\frac{4}{81}-\frac{5}{243} $$

In \(15-26,\) write the first five terms of each geometric sequence. $$ a_{1}=1, a_{3}=16 $$

In \(19-24 :\) a. Write each arithmetic series as the sum of terms. b. Find the sum. $$ \sum_{n=1}^{10}(-1+2 n) $$

In \(19-30 :\) a. Write an algebraic expression that represents \(a_{n}\) for each sequence. b. Find the ninth term of each sequence. $$ 7,9,11,13, \dots $$