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Section 2

Arithmetic Sequences

If the given sequence is arithmetic, find the common difference d. If the sequence is not arithmetic, say so.$$1,2,3,4,5, \ldots$$

If the given sequence is arithmetic, find the common difference d. If the sequence is not arithmetic, say so.$$2,5,8,11, \ldots$$

If the given sequence is arithmetic, find the common difference d. If the sequence is not arithmetic, say so.$$2,-4,6,-8,10,-12, \dots$$

If the given sequence is arithmetic, find the common difference d. If the sequence is not arithmetic, say so.$$1,2,4,7,11,16, \dots$$

If the given sequence is arithmetic, find the common difference d. If the sequence is not arithmetic, say so.$$10,5,0,-5,-10, \dots$$

If the given sequence is arithmetic, find the common difference d. If the sequence is not arithmetic, say so.$$-6,-10,-14,-18, \dots$$

Write the first five terms of each arithmetic sequence.$$a_{1}=5, d=4$$

Write the first five terms of each arithmetic sequence.$$a_{1}=6, d=7$$

Write the first five terms of each arithmetic sequence.$$a_{1}=-2, d=-4$$

Write the first five terms of each arithmetic sequence.$$a_{1}=-3, d=-5$$

Use the formula for $a_{n}$ to find the general term of each arithmetic sequence.$$a_{1}=2, d=5$$

Use the formula for $a_{n}$ to find the general term of each arithmetic sequence.$$a_{1}=5, d=3$$

Use the formula for $a_{n}$ to find the general term of each arithmetic sequence.$$3, \frac{15}{4}, \frac{9}{2}, \frac{21}{4}, \dots$$

Use the formula for $a_{n}$ to find the general term of each arithmetic sequence.$$1, \frac{5}{3}, \frac{7}{3}, 3, \ldots$$

Use the formula for $a_{n}$ to find the general term of each arithmetic sequence.$$-3,0,3, \dots$$

Use the formula for $a_{n}$ to find the general term of each arithmetic sequence.$$-10,-5,0, \ldots$$

Evaluate the indicated term for each arithmetic sequence.$$a_{1}=4, d=3 ; a_{25}$$

Evaluate the indicated term for each arithmetic sequence.$$a_{1}=1, d=-3 ; \quad a_{12}$$

Evaluate the indicated term for each arithmetic sequence.$$2,4,6, \ldots ; \quad a_{24}$$

Evaluate the indicated term for each arithmetic sequence.$$1,5,9, \ldots ; a_{50}$$

Evaluate the indicated term for each arithmetic sequence.$$a_{12}=-45, a_{10}=-37 ; \quad a_{1}$$

Evaluate the indicated term for each arithmetic sequence.$$a_{10}=-2, a_{15}=-8 ; \quad a_{3}$$

Evaluate the number of terms in each arithmetic sequence.$$3,5,7, \ldots, 33$$

Evaluate the number of terms in each arithmetic sequence.$$4,1,-2, \dots,-32$$

Evaluate the number of terms in each arithmetic sequence.$$\frac{3}{4}, 3, \frac{21}{4}, \dots, 12$$

Evaluate the number of terms in each arithmetic sequence.$$2, \frac{3}{2}, 1, \frac{1}{2}, \ldots,-5$$

In the formula for $S_{n},$ what does $n$ represent?

Explain when you would use each of the two formulas for $S_{n}$.

Evaluate $S_{6}$ for each arithmetic sequence.$$a_{1}=6, d=3$$

Evaluate $S_{6}$ for each arithmetic sequence.$$a_{1}=5, d=4$$

Evaluate $S_{6}$ for each arithmetic sequence.$$a_{1}=7, d=-3$$

Evaluate $S_{6}$ for each arithmetic sequence.$$a_{1}=-5, d=-4$$

Evaluate $S_{6}$ for each arithmetic sequence.$$a_{n}=4+3 n$$

Evaluate $S_{6}$ for each arithmetic sequence.$$a_{n}=9+5 n$$

Use a formula for $S_{n}$ to evaluate each series.$$\sum_{i=1}^{10}(8 i-5)$$

Use a formula for $S_{n}$ to evaluate each series.$$\sum_{i=1}^{17}(3 i-1)$$

Use a formula for $S_{n}$ to evaluate each series.$$\sum_{i=1}^{20}\left(\frac{3}{2} i+4\right)$$

Use a formula for $S_{n}$ to evaluate each series.$$\sum_{i=1}^{11}\left(\frac{1}{2} i-1\right)$$

Use a formula for $S_{n}$ to evaluate each series.$$\sum_{i=1}^{250} i$$

Use a formula for $S_{n}$ to evaluate each series.$$\sum_{i=1}^{2000} i$$

Solve each problem.Nancy Bondy's aunt has promised to deposit $\$ 1$ in her account on the first day of her birthday month, $\$ 2$ on the second day, $\$ 3$ on the third day, and so on for 30 days. How much will this amount to over the entire month?

Solve each problem.Repeat Exercise 41 , but assume that the deposits are 2 Dollar, 4 Dollar, 6 Dollar, and so on, and that the month is February of a leap year.

Solve each problem.Suppose that Cherian Mathew is offered a job at $\$ 1600$ per month with a guaranteed increase of $\$ 50$ every six months for 5 yr. What will Cherian's salary be at the end of that time?

Solve each problem.Repeat Exercise $43,$ but assume that the starting salary is $\$ 2000$ per month and the guaranteed increase is $\$ 100$ every four months for 3 yr.

Solve each problem.A seating section in a theater-in-the-round has 20 seats in the first row, 22 in the second row, 24 in the third row, and so on for 25 rows. How many seats are there in the last row? How many seats are there in the section?

Solve each problem.Constantin Arne has started on a fitness program. He plans to jog 10 min per day for the first week and then add 10 min per day each week until he is jogging an hour each day. In which week will this occur? What is the total number of minutes he will run during the first four weeks?

Solve each problem.A child builds with blocks, placing 35 blocks in the first row, 31 in the second row, 27 in the third row, and so on. Continuing this pattern, can she end with a row containing exactly 1 block? If not, how many blocks will the last row contain? How many rows can she build this way?

Solve each problem.A stack of firewood has 28 pieces on the bottom, 24 on top of those, then $20,$ and so on. If there are 108 pieces of wood, how many rows are there? (Hint: $n \leq 7$.)

Evaluate ar $^{n}$ for the given values of $a, r,$ and $n$$$a=2, r=3, n=2$$

Evaluate ar $^{n}$ for the given values of $a, r,$ and $n$$$a=3, r=2, n=4$$

Evaluate ar $^{n}$ for the given values of $a, r,$ and $n$$$a=4, r=\frac{1}{2}, n=3$$

Evaluate ar $^{n}$ for the given values of $a, r,$ and $n$$$a=5, r=\frac{1}{4}, n=2$$