12 2 Arithmetic Sequences 2001 by R Villar
12. 2 Arithmetic Sequences © 2001 by R. Villar All Rights Reserved
Arithmetic Sequences Arithmetic Sequence: sequence whose consecutive terms have a common difference. Example: 3, 5, 7, 9, 11, 13, . . . The terms have a common difference of 2. The common difference is the number d. Example: Is the sequence arithmetic? – 45, – 30, – 15, 0, 15, 30 Yes, the common difference is 15 How do you find any term in this sequence? To find any term in an arithmetic sequence, use the formula an = a 1 + (n – 1)d where d is the common difference.
Example: Find a formula for the nth term of the arithmetic sequence in which the common difference is 5 and the first term is 3. an = a 1 + (n – 1)d a 1 = 3 d = 5 an = 3 + (n – 1)5
Example: If the common difference is 4 and the fifth term is 15, what is the 10 th term of an arithmetic sequence? an = a 1 + (n – 1)d We need to determine what the first term is. . . d=4 and a 5 = 15 a 5 = a 1 + (5 – 1)4 = 15 a 1 = – 1 a 10 = – 1 + (10 – 1)4 a 10 = 35
Determine whether each sequence appears to be an arithmetic sequence. If so, find the common difference and the next three terms in the sequence. A. 12, 8, 4, 0, … B. 1, 4, 9, 16, …
Find the indicated term of each arithmetic sequence. A. 22 nd term: 5, 2, -1, -4, … B. 15 th term: a 1 = 7; d = 3
a. Find the next three terms of the arithmetic sequence 0, 9, 18, 27, … b. Find the 7 th term of the arithmetic sequence 10, 23, 36, . . .
Which of the following is the 24 th term of the arithmetic sequence 3, 2, 7, 12, . . . ? A 62 B 92 C 112 D 162
100 Category 1 3, 6, 9, ___, ___ Answer
Answer 100 Category 1 3, 6, 9, 12, 15, 18
200 Category 1 20, 12, 4 , ___, ___ Answer
Answer 200 Category 1 20, 12, 4 , -4, -12, -20
300 Category 1 800, 400, 200, , ___, ___ Answer
Answer 300 Category 1 800, 400, 200, 100, 50, 25
400 Category 1 3, 5, 8, 12, ___, ___ Answer
Answer 400 Category 1 3, 5, 8, 12, 17, 23, 30
500 Category 1 1, 1, 2, 3, 5, 8 , ___, ___ Answer
Answer 500 Category 1 1, 1, 2, 3, 5, 8 , 13, 21, 34
100 Category 2 Write the rule if a 1= 10 d = 3 Answer
Answer 100 Category 2 Write the rule if a 1= 10 d = 3 an = 7 + 3 n
200 Category 2 Write the rule if a 3= 15 d = -2 Answer
Answer 200 Category 2 Write the rule if a 3= 15 d = -2 an = 21 - 2 n
300 Category 2 Write the first 5 terms for an=6+5 n Answer
Answer 300 Category 2 Write the first 5 terms for an=6+5 n 11, 16, 21, 26, 31
400 Category 2 Find a 20 for 10, 6, 2, -2. . . Answer
Answer 400 Category 2 Find a 20 for 10, 6, 2, -2… an =14 - 4 n so a 20 = 14 - 4(20) = -66
500 Category 2 Find the rule if a 3 = 5 and a 7 = 9 Answer
Answer 500 Category 2 Find the rule if a 3 = 5 and a 7 = 9 __, 5, __, __, 9 d = (9 -5)/(7 -3) =1 an = 2 +1 n
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