Ch. 12 Review
1.Find the first four terms of the sequence .
Write the next three terms of the arithmetic sequence. Then write a variable expression for the nth term and evaluate it for
2.
Write the next three terms of the geometric sequence. Then write a variable expression for the nth term and evaluate it for
3.49; 343; 2401; 16,807; . . .
Write the series with summation notation.
4.
5.
6.
Find the sum of the series.
7.
8.
Write a rule for the nth term of the arithmetic sequence.
9.–12, –5, 2, 9, . . .
10.Write a rule for the nth term of the arithmetic sequence.
16, 19, 22, . . .
11.Write a rule for the nth term of the arithmetic sequence with and the common difference of .
12.What is the first term of an arithmetic sequence with a common difference of 5 and a sixth term of 40?
13.Find the sum of the first nine terms of the arithmetic series.
. . .
Evaluate.
14.
15.Find the sum of the first 30 terms of the arithmetic series.
9 + 17 + 25 + 33 + . . .
16.Evaluate the sum.
17.Evaluate the sum.
18.Tell whether the sequence is arithmetic. If it is find the common difference.
a.
b.
19.Two terms of an arithmetic sequence are and . Find a rule for the nth term.
20.Identify the sequence as arithmetic, geometric, or neither.
1, 1, 2, 6, 24, 120, . . .
21.Identify the sequence as arithmetic, geometric, or neither.
1, 4, 9, 16, 25, . . .
22.Explain the difference between an arithmetic sequence and a geometric sequence.
Write a rule for the nth term of the geometric sequence.
23.. . .
24. . . .
25.Find the first 4 terms of the geometric sequence for which and
Write a rule for the nth term of the geometric sequence.
26.and
Evaluate.
27.Find the sum of the finite geometric series. Round your result to two decimal places.
28.Identify the next three terms in the sequence. 4, 20, 100, 500, . . .
29.Find the missing number in the following pattern.
, , , , , _____
30.Find the common ratio of the geometric sequence.
2, –8, 32, –128, . . .
31.Two terms of a geometric sequence are and . Find a rule for the nth term.
32.Find the sum of the infinite geometric series .
Find the sum of the infinite geometric series if it has a sum.
33.
34.Which of the infinite geometric series does not have a sum? Explain
A. B.
35.Which of the infinite geometric series does not have a sum? Explain.
A. B.
Tell whether the series has a sum. Write Yes or No. If it does, give its value.
36.5+++...
37.25+++...
Find the common ratio of an infinite geometric series with the given sum and first term.
38.
39.
Find the sum of the geometric series.
40.24+...
____41.32+...
a. / / c. /b. / / d. /
Write the repeated decimal as a fraction in simplest terms.
42. 13.13131313
43. 0.4545454545
44. 0.122122122122
Ch. 12 Review
Answer Section
1.ANS:8, 22, 42, 68DIF:Level A
3.ANS:
DIF:Level B
4.ANS:117,649; 823,543; 5,764,801;; 282,475,249
DIF:Level C
5.ANS:DIF:Level B
6.ANS:DIF:Level B
7.ANS:DIF:Level B
8.ANS:0 + 3 + 8 + 15; 26DIF: Level B
9.ANS:3 + 6 + 11 + 18; 38DIF: Level B
10.ANS:DIF:Level B
12.ANS: DIF: Level B
13.ANS:DIF:Level B
15.ANS:15DIF:Level B
17.ANS:DIF:Level B
19.ANS:286DIF:Level B
21.ANS:3750DIF:Level B
22.ANS:430DIF:Level B
24.ANS:DIF:Level B
25.ANS:a. yes, DIF:Level A
b. yes,
26.ANS:DIF:Level B
27.ANS:NeitherDIF:Level B
29.ANS:NeitherDIF:Level B
30.ANS:Sample answer: In an arithmetic sequence, each term after the first term is found by adding or subtracting the same number from the previous term, while in a geometric sequence, each term after the first term is found by multiplying the previous term by the same number. DIF: Level A
31.ANS:DIF:Level B
33. ANS: DIF: Level B
34. ANS: –9, –45, –225, –1125DIF: Level B
35. ANS: DIF: Level B
38. ANS: DIF: Level B
39. ANS: 2500, 12,500, 62,500 DIF: Level B
40. ANS: DIF:Level B
41. ANS: –4DIF:Level A
44. ANS: DIF: Level B
45. ANS: DIF:Level B
47. ANS: DIF:Level B
50. ANS: B. because 1
DIF: Level B
51. ANS: B. because
DIF: Level B
52. ANS: NoDIF:Level B
53. ANS: Yes; DIF:Level B
54. ANS: DIF:Level B
55. ANS: DIF:Level B
57. ANS: DIF:Level B
58. ANS: DDIF:Level B