What’s My Pattern? Math 8 Unit 4 Task 1. For each list of numbers below, determine the next three numbers in the list. a. 1, 2, 3, 4, 5, _______, _______, _______ b. 7, 9, 11, 13, 15, _______, _______, _______ c. 10, 7, 4, 1, 2, _______, _______, _______ d. 2, 4, 7, 11, 16, _______, _______, _______ e. 1, 1, 2, 2, 3, 3, _______, _______, _______ f. 0, 1, 4, 9, 16, 25, _______, _______, _______ g. 2.0, 3.5, 5.0, 6.5, 8.0, 9.5, _______, _______, _______ h. 17.5, 13.2, 8.9, 4.6, 0.3, _______, _______, ________ i. 2, 5, 11, 23, 47, _______, _______, _______ j. 1, 1, 2, 3, 5, 8, _______, _______, _______ 2. If the name of each sequence below refers to the letter part of the sequences given in question 1, fill in the blanks for the following equations. a3 =________
c5 =________
g 7 = ________
a31 =________
e________ = −1
3. Your answers to the lists of numbers (sequences) in question 1 numerically described the patterns you noticed. Now use words to describe the patterns you noticed in each of the sequences for question 1. Whenever possible, identify what is done to each term in the sequence to determine the next term in the sequence.
4. Match the following sequences to their recursive definitions.
________
________
________
1, 2, 3, 4, 5, …
t1 = 1 A. t n = t n− 1 − 2
1, 1, 3, 5, 7, …
t1 = 7 B. tn = tn− 1 − 2
7, 5, 3, 1, …
t1 = 1 C. t n = t n− 1 + 1
_______
7, 11, 17, 25, …
t1 = 7 D. t n = t n − 1 + 2n
5. Write a recursive definition for each of the following sequences. A.
7, 9, 11, 13, 15, …
B.
10, 7, 4, 1, 2, …
C.
2.0, 3.5, 5.0, 6.5, 8.0, 9.5 …
D.
2, 4, 7, 11, 16, …
E.
0, 1, 4, 9, 16, 25, …