Tell whether the sequence is linear. If it is, find the next two terms. If it is not explain why not.
1) \( 22,19,16,13,10,... \)
2) \( 2,8,32,128,512,... \)
3) \( 63,50,37,24,11,... \)
1) \( 22,19,16,13,10,... \)
2) \( 2,8,32,128,512,... \)
3) \( 63,50,37,24,11,... \)
Given the table, graph the sequence and comment on whether it is a linear relationship.
4) \(\begin{array}{|c|c|c|c|c|c|} \hline x & 1 & 2 & 3 & 4 & 5\\ \hline f(x) & \dfrac{3}{2} & 2 & \dfrac{5}{2} & 3 & \dfrac{7}{2} \\ \hline \end{array}\)
5) \(\begin{array}{|c|c|c|c|c|c|} \hline x & 2 & 3 & 5 & 6 & 8\\ \hline f(x) & 2.6 & 2.3 & 2 & 1.7 & 1.4\\ \hline \end{array}\)
6) \(\begin{array}{|c|c|c|c|c|c|} \hline x & 1 & 2 & 3 & 4 & 5 & 6 & 7\\ \hline f(x) & \text{-}3.4 &\text{-}2.9 & \text{-}2.4 & \text{-}1.9 & \text{-}1.4 &\text{-}0.9 & \text{-}0.4\\ \hline \end{array}\)
7) \(\begin{array}{|c|c|c|c|c|c|c|} \hline x & 6 & 5 & 4 & 3 & 2 & 1 & 0\\ \hline f(x) & 8 & 7 & 6 & 4 & 3 & 1 & 0\\ \hline \end{array}\)
8) \(\begin{array}{|c|c|} \hline x & f(x)\\ \hline 1 & 2 \\ \hline 3 & 4\\ \hline 5 & 6\\ \hline 6 & \dfrac{29}{4}\\ \hline 7 & \dfrac{19}{2}\\ \hline 8 & \dfrac{47}{4}\\ \hline 9 & 14\\ \hline \end{array}\)
4) \(\begin{array}{|c|c|c|c|c|c|} \hline x & 1 & 2 & 3 & 4 & 5\\ \hline f(x) & \dfrac{3}{2} & 2 & \dfrac{5}{2} & 3 & \dfrac{7}{2} \\ \hline \end{array}\)
5) \(\begin{array}{|c|c|c|c|c|c|} \hline x & 2 & 3 & 5 & 6 & 8\\ \hline f(x) & 2.6 & 2.3 & 2 & 1.7 & 1.4\\ \hline \end{array}\)
6) \(\begin{array}{|c|c|c|c|c|c|} \hline x & 1 & 2 & 3 & 4 & 5 & 6 & 7\\ \hline f(x) & \text{-}3.4 &\text{-}2.9 & \text{-}2.4 & \text{-}1.9 & \text{-}1.4 &\text{-}0.9 & \text{-}0.4\\ \hline \end{array}\)
7) \(\begin{array}{|c|c|c|c|c|c|c|} \hline x & 6 & 5 & 4 & 3 & 2 & 1 & 0\\ \hline f(x) & 8 & 7 & 6 & 4 & 3 & 1 & 0\\ \hline \end{array}\)
8) \(\begin{array}{|c|c|} \hline x & f(x)\\ \hline 1 & 2 \\ \hline 3 & 4\\ \hline 5 & 6\\ \hline 6 & \dfrac{29}{4}\\ \hline 7 & \dfrac{19}{2}\\ \hline 8 & \dfrac{47}{4}\\ \hline 9 & 14\\ \hline \end{array}\)
Determine if the situation represents a linear relationship? Justify your answer.
9) If your dorm room was \(70\) degrees and you and your roommate were cold. So you decided to increase it by two degrees. An hour later your roommate turned it up again to \(74\). Another hour passed and you consulted with your roommate and you decided to increase it by two more degrees to \(76\).
10) You decided to train for a \(100\) mile bike ride. To reach your goal you set out on a \(25\) week training schedule. The "big rides" each week are on Saturday. They start at \(50\) miles and increase by two miles each week.
11) You inherited \(\$10,000\) from your great-great-great grandfather that was given to you on your 16th birthday. You decided to spend \(10\%\) of what is in the account each year. (The account does not get any interest)
12) You take your car to the car wash. You put \(\$4.00\) worth of change into the machine and it runs for 5 minutes and shuts off. Then you put another \(\$4.00\) worth of change into the machine and it runs for another 5 minutes.
13) Measure some pattern with a ruler to find a real world arithmetic sequence. Report where you found it, what the common difference is, and what the measures of the sequence are for the first \(5\) terms.
9) If your dorm room was \(70\) degrees and you and your roommate were cold. So you decided to increase it by two degrees. An hour later your roommate turned it up again to \(74\). Another hour passed and you consulted with your roommate and you decided to increase it by two more degrees to \(76\).
10) You decided to train for a \(100\) mile bike ride. To reach your goal you set out on a \(25\) week training schedule. The "big rides" each week are on Saturday. They start at \(50\) miles and increase by two miles each week.
11) You inherited \(\$10,000\) from your great-great-great grandfather that was given to you on your 16th birthday. You decided to spend \(10\%\) of what is in the account each year. (The account does not get any interest)
12) You take your car to the car wash. You put \(\$4.00\) worth of change into the machine and it runs for 5 minutes and shuts off. Then you put another \(\$4.00\) worth of change into the machine and it runs for another 5 minutes.
13) Measure some pattern with a ruler to find a real world arithmetic sequence. Report where you found it, what the common difference is, and what the measures of the sequence are for the first \(5\) terms.
#14-16 Which of the following visual patterns would be a linear relationship? Justify your answer
17) If any of the visual patterns have a linear relationship, find how many squares are in Step 10.
Review
18) Graph \(y = -\dfrac{2}{3}x + 11\)
19) Graph \(-5x + 2y = -20\)
20) Graph \(y - 1 = \dfrac{7}{4}(x + 8)\)
Solution Bank
Review
18) Graph \(y = -\dfrac{2}{3}x + 11\)
19) Graph \(-5x + 2y = -20\)
20) Graph \(y - 1 = \dfrac{7}{4}(x + 8)\)
Solution Bank