Algebra 2 CP
Chapter 12 Test Review
Name________________
Date_________________
Decide whether the sequence is arithmetic, geometric or neither. If it is arithmetic, state the
value of d. If it is geometric, state the value of r. Lastly, find the next two terms of the
sequence.
1. 9, 16, 23, 30, …
2. 1, 2, 4, 7, …
3. 1, 4, 16, 64, …
1._______________
2._______________
3._______________
_________________
_________________
_________________
4.
500, 100, 20, 4,…
5.
1 2 3 4
, , , ,...
2 3 4 5
6.
28, 19, 10, 1,…
4._______________
5._______________
6._______________
_________________
_________________
_________________
Write a rule for the nth term of the arithmetic sequence. Then find a20.
2 4
8
7. 6, 2, -2, -6, -10,…
8. 0, , , 2, ,...
9.
3 3
3
1.5, 3.6, 5.7, 7.8,…
7._______________
8._______________
9._______________
_________________
_________________
_________________
Write a rule for the nth term of the geometric sequence.
10. 256, 64, 16, 4, 1,…
11. r  5 , a2  200
12. a1  144 , a3  16
10._______________
12._______________
11._______________
Write a rule for the nth term of the arithmetic sequence.
1
1
and d  
2
2
13. a6  16 and d  9
14. a11 
13._______________
14._______________
15. a10  148 and a44  556
16. a8  10 and a20  58
15._______________
16._______________
Find the sum of the series. If the series is arithmetic or geometric, use the formulas
from section 12.2 – 12.4. If the series is neither, just find the sum by adding the terms.
 n
6
17.
2
 7
6
18.
n2
n 1
17.______________
18.______________
32
21.
1
n 1
21.______________
 10  4n 
10
22.
n
2
n 3
22.______________
30
19.
 8n  84
n 1
19.______________
1
23.  40 
2
n 1
7
n 1
23.______________
6
20.
 35
n 1
n 1
20._____________
 1
24. 12  
 2
n 0
7
n
24._____________

25.
1
3 

n 1  4 
n 1
25._____________

26.
2
 5 

5
n 1
n 1

27.
26._____________

5 n
3

n 0 6
28.
27._____________
3
 6 

2
n 1
28._____________
Find the common ratio of the infinite geometric series with the given sum and first term.
29. S = 7, a1 = 2
30. S = 12, a1 = 3
29._________________
31. S =
30._________________
24
, a1 = 3
5
32. S =
31._________________
2
, a1 = ½
3
32._________________
Write the following repeating decimals as fractions. You MUST show all work!
33. 0.282828…
34. 0.55555…
35. 0.168168168…
33._____________
34._____________
Write the first five terms of the sequence.
36.
a0  4
a n  2a n 1
36.______________
37.
a0  3
a n  a n1  n 2
37.______________
n
35._____________
a0  2
38. a1  4
a n  a n 1  a n  2
38._____________
Write a recursive rule for the sequence. The sequence may be arithmetic, geometric, or
neither.
39. 3, 12, 48, 192, 768,…
40. 4, 6, 9, 13, 18,…
41. 7, 13, 19, 25, 31,…
39._______________
40._______________
41._______________
42. 135, 45, 15, 5,…
43. 1, -3, 9, -27,…
44. 3, 5, 15, 75, 1125,…
42._______________
43._______________
44._______________
Find the first three iterates of the function for the given initial value.
44. f(x) = x + 3, x0 = 0
45. f(x) = 2x – 7, x0 = 8
46. f(x) = x2 + 3, x0 = 1
44._______________
45._______________
46._______________
47. An auditorium has 25 rows. The first row has 10 seats, and each row after that has 1 more seat
than the row before it.
a. Write a rule for the number of seats in the nth row
b.
Find the total number of seats in the auditorium
48. You drop a ball from a height of 66 inches and the ball starts bouncing. After each bounce, the
ball reaches a height that is 80% of the previous height. Write a rule for the height of the ball
after the nth bounce. Then find the height of the ball after the sixth bounce.
49. A pendulum is released. It swings forward traveling a distance of 120 centimeters. On each
successive swing, the pendulum travels 97% of the distance of the previous swing. Find the
total distance traveled by the pendulum in the first 12 swings.
50. A ball is dropped from a height of 40 feet. Each time it hits the ground, it bounce three-fourths
of its previous height. Find the total distance the ball has traveled before coming to rest.
Answers
1.
Arithmetic
d = 7; 37, 44
2.
Neither
11, 16
3.
Geometric
r = 4; 256, 1024
4. Geometric
r = 1/5; 4/5, 4/25
5.
Neither
5/6, 6/7
6.
Arithmetic
d = -9; -8, -17
7.
an = 10 – 4n
a20 = -70
8.
9.
an = -0.6 + 2.1n; a20 = 41.4
1
12. a n  144 
 3
1
10. a n  256 
4
n 1
an = (2/3)n – 2/3
a20 = 38/3
11. an  405
n1
n 1
13. an = -70 + 9n
14. an = 6 – ½n
15. an = 12n + 28
16. an = -4n + 22
17. 133
18. -30
19. 1200
20. 11,718
21. 32
22. 380
23. 635/8
24. 255/32
25. 4
26. -25/3
27. No Sum
28. No Sum
29. r = 5/7
30. r = ¾
31. r = 3/8
32. r = ¼
33. 28/99
34. 5/9
35. 56/333
36. 4, 8, 16, 32, 64
37. 3, 2, -2, -11, -27
38. 2, 4, 2, -2, -4
39. a1 = 3
an = 4an – 1
40. a1 = 4
an = a n – 1 + n
42. a1 = 135
an = 1/3an – 1
43. a1 = 1
an = -3an – 1
44. a1 = 3, a2 = 5 44. 3, 6, 9
an = a n – 1 · an – 2
46. 4, 19, 364
47. a) an = 9 + n; b) 550 seats
 1
a n  144  
 3
n 1
48. an  660.8 ; 17.3 inches
n
41. a1 = 7
a n = an – 1 + 6
49. 1224.6 cm
45. 9, 11, 15
50. 280 feet