Determine whether the sequence is arithmetic, geometric, or neither. 18, 11, 4,


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1 Over Lesson 10 1 Determine whether the sequence is arithmetic, geometric, or neither. 18, 11, 4, A. arithmetic B. geometric C. neither
2 Over Lesson 10 1 Determine whether the sequence is arithmetic, geometric, or neither. 18, 11, 4, A. arithmetic B. geometric C. neither
3 Over Lesson 10 1 Determine whether the sequence is arithmetic, geometric, or neither. 1, 2, 4, 8, A. arithmetic B. geometric C. neither
4 Over Lesson 10 1 Determine whether the sequence is arithmetic, geometric, or neither. 1, 2, 4, 8, A. arithmetic B. geometric C. neither
5 Over Lesson 10 1 Determine whether the sequence is arithmetic, geometric, or neither. 5, 6, 8, 11, A. arithmetic B. geometric C. neither
6 Over Lesson 10 1 Determine whether the sequence is arithmetic, geometric, or neither. 5, 6, 8, 11, A. arithmetic B. geometric C. neither
7 Over Lesson 10 1 Find the next three terms of the sequence. 25, 50, 75, 100, A. 125, 150, 175 B. 125, 250, 500 C. 125, 145, 175 D. 150, 200, 225
8 Over Lesson 10 1 Find the next three terms of the sequence. 25, 50, 75, 100, A. 125, 150, 175 B. 125, 250, 500 C. 125, 145, 175 D. 150, 200, 225
9 Over Lesson 10 1 Find the next three terms of the sequence. 1, 6, 36, 216, A. 236, 266, 336 B. 306, 336, 416 C. 1296, 7776, 46,656 D. 1296, 3888, 11,664
10 Over Lesson 10 1 Find the next three terms of the sequence. 1, 6, 36, 216, A. 236, 266, 336 B. 306, 336, 416 C. 1296, 7776, 46,656 D. 1296, 3888, 11,664
11 Over Lesson 10 1 Find the first term and the ninth term of the arithmetic sequence., 4.5, 7, 9.5, 12, A. 2; 14.5 B. 2.5; 22 C. 2; 22 D. 2.5; 14.5
12 Over Lesson 10 1 Find the first term and the ninth term of the arithmetic sequence., 4.5, 7, 9.5, 12, A. 2; 14.5 B. 2.5; 22 C. 2; 22 D. 2.5; 14.5
13
14 arithmetic means series arithmetic series partial sum sigma notation
15
16 Find the nth Term Find the 20th term of the arithmetic sequence 3, 10, 17, 24,. Step 1 Find the common difference = = = 7 So, d = 7.
17 Find the nth Term Step 2 Find the 20th term. a n = a 1 + (n 1)d nth term of an arithmetic sequence a 20 = 3 + (20 1)7 a 1 = 3, d = 7, n = 20 = or 136 Simplify. Answer: The 20th term of the sequence is 136.
18 Find the 17th term of the arithmetic sequence 6, 14, 22, 30,. A. 134 B. 140 C. 146 D. 152
19 Write Equations for the nth Term A. Write an equation for the nth term of the arithmetic sequence below. 8, 6, 4, d = 6 ( 8) or 2; 8 is the first term. a n = a 1 + (n 1)d Answer: a n = 2n 10 nth term of an arithmetic sequence a n = 8 + (n 1)2 a 1 = 8 and d = 2 a n = 8 + (2n 2) a n = 2n 10 Distributive Property Simplify.
20 Write Equations for the nth Term B. Write an equation for the nth term of the arithmetic sequence below. a 6 = 11, d = 11 First, find a 1. a n = a 1 + (n 1)d nth term of an arithmetic sequence 11 = a 1 + (6 1)( 11) a 6 = 11, n = 6, and d = = a 1 55 Multiply. 66 = a 1 Add 55 to each side.
21 Then write the equation. a n = a 1 + (n 1)d Write Equations for the nth Term nth term of an arithmetic sequence a n = 66 + (n 1)( 11) a 1 = 66, and d = 11 a n = 66 + ( 11n + 11) a n = 11n + 77 Distributive Property Simplify. Answer: a n = 11n + 77
22 A. Write an equation for the nth term of the arithmetic sequence below. 12, 3, 6, A. a n = 9n 21 B. a n = 9n 21 C. a n = 9n + 21 D. a n = 9n + 21
23 B. Write an equation for the nth term of the arithmetic sequence below. a 4 = 45, d = 5 A. a n = 5n + 25 B. a n = 5n 20 C. a n = 5n + 40 D. a n = 5n + 30
24 Find Arithmetic Means Find the arithmetic means in the sequence 21,,,, 45,. Step 1 Step 2 Find d. a n = a 1 + (n 1)d Since there are three terms between the first and last terms given, there are or 5 total terms, so n = 5. Formula for the nth term 45 = 21 + (5 1)d n = 5, a 1 = 21, a 5 = = d Distributive Property 24 = 4d Subtract 21 from each side. 6 = d Divide each side by 4.
25 Find Arithmetic Means Step 3 Use the value of d to find the three arithmetic means Answer:
26 Find the three arithmetic means between 13 and 25. A. 16, 19, 22 B. 17, 21, 25 C. 13, 17, 21 D. 15, 17, 19
27
28 Use the Sum Formulas Find the sum Step 1 a 1 = 8, a n = 80, and d = 12 8 or 4. We need to find n before we can use one of the formulas. a n = a 1 + (n 1)d nth term of an arithmetic sequence 80 = 8 + (n 1)(4) a n = 80, a 1 = 8, and d = 4 80 = 4n + 4 Simplify. 19 = n Solve for n.
29 Use the Sum Formulas Step 2 Use either formula to find S n. Sum formula a 1 = 8, n = 19, d = 4 Simplify. Answer: 836
30 Find the sum A. 318 B. 327 C. 340 D. 365
31 Find the First Three Terms Find the first three terms of an arithmetic series in which a 1 = 14, a n = 29, and S n = 129. Step 1 Since you know a 1, a n, and S n, use to find n. Sum formula S n = 129, a 1 = 14, a n = 29 Simplify. Divide each side by 43.
32 Step 2 Find d. Find the First Three Terms a n = a 1 + (n 1)d nth term of an arithmetic sequence 29 = 14 + (6 1)d a n = 29, a 1 = 14, n = 6 15 = 5d Subtract 14 from each side. 3 = d Divide each side by 5.
33 Find the First Three Terms Step 3 Use d to determine a 2 and a 3. a 2 = or 17 a 3 = or 20 Answer: The first three terms are 14, 17, and 20.
34 Find the first three terms of an arithmetic series in which a 1 = 11, a n = 31, and S n = 105. A. 16, 21, 26 B. 11, 16, 21 C. 11, 17, 23, 30 D. 17, 23, 30, 36
35
36 Use Sigma Notation Evaluate. A. 23 B. 70 C. 98 D. 112 Read the Test Item You need to find the sum of the series. Find a 1, a n, and n.
37 Use Sigma Notation Method 1 Since the sum is an arithmetic series, use the formula. There are 8 terms. a 1 = 2(3) + 1 or 7, and a 8 = 2(10) + 1 or 21
38 Solve the Test Item Method 2 Use Sigma Notation Find the terms by replacing k with 3, 4,..., 10. Then add.
39 Evaluate. A. 85 B. 95 C. 108 D. 133
40
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