PreCalculus
Ch. 10 Review
Name_______________________
Period _______
* Show work on the separate sheet of paper.
[1-3] Find the specified term of each sequence.
1
2
2n
1.
6th term: an 
3.
4th term: a1  7, an  2an1  n
2.
3rd term: a1  9, an 
an 1
3
[4-5] Find the indicated sum for each sequence.
4.
7th partial sum of 1, 4, 9, 16, …
5.
fourth partial sum of an 
2an 1
, a1  1
5
[6-7] Determine whether each sequence is convergent or divergent. Explain why.
6. 20, 18, 14, 8, …
7. an 
(1)n
2n  1
[8-9] Find each sum.
7
25
8.
 (2n  5)
9.
n4
i2  2

i 3
[10-11] Find a recursive formula and an explicit formula for each sequence.
1 3 9 27
, , ,
,...
2 2 2 2
[12-15] Find the specified value for the arithmetic sequence with the given characteristics.
10.
12.
13.
14.
15.
 4,  1, 2, 5, …
If
If
If
If
11.
a1  27 and d  3, find a24
an  27, a1  12, and d  3, find n.
a23  32 and a1  12, find d .
a6  5 and a10  7, find a1
[16-17] Find the indicated arithmetic means for each set of nonconsecutive terms.
16. 3 means: 35 and 45
17. 7 means:  2 and 16
18. Find a quadratic model for the sequence 8, 16, 26, 38, 52, 68.
19. Find the sum of the series 7+10+13+…+79.
20. Find the 53rd partial sum of the arithmetic series 12+20+28+…
15
21. Find
 (3n  1).
n 3
42
22. Find
2n.

n 1
23. Find r and 7th term of the geometric sequence 8,  24, 72, …
24. Find the first term of the geometric sequence for which a6  0.1, r  0.2
25. Find r of the geometric sequence for which a1  15, a10  7680.
26. Create the rule of the geometric sequence for which a3  9.2, a5  36.8
27. Write a sequence that has two geometric means between 6 and 162.
[28-32] Find each sum.
3 9
27
28. s8 of 

 ...
4 20 100

11
29.
 2(1.5)n1
 6( 3)
n2
32.
10  5  2.5  ...
n 3

31.
3

n 1
n 1
1
30.
n 1
33. CVHS auditorium has 26 rows. The first row has 22 seats. The number of seats in each row
increases by 4 as you move to the back of the auditorium.
a) How many seats are in the last row?
b) What is the seating capacity of this auditorium?
34. The first year salary of an employee is $34,500. Each year thereafter, her annual salary increases
by $750.
a) What will her salary be during her 10th year of work?
b) What will her total earnings be for 25 years of work?
35. An employee agreed to a salary plan where his annual salary increases by 4.5% each year.
He earned $50,081 for his tenth year of work.
a) What was his pay for his first year of work?
b) How much did he earn for his first 10 years of work?
36. A city of 100,000 people is growing at a rate of 5.2% per year. Assuming this growth rate remains
constant, estimate the population of the city five years from now.
<Keys> -----------------------------------------------------------------------------------------------------1
25
87
or
1. 2
2. 1
3. 74
4. 140
5.
6. divergent
7. convergent
12
12
125
8. 528 9. 125
10. a1  4, an  an1  3 for n  2 : an  7  3n
1
1
11. a1  , an  3an 1 for n  2 : an  (3) n 1 12. 42
13. 14
14. 2
15. 20
2
2
16. 37.5, 40, 42.5
17. 0.25, 2.5, 4.75, 7, 9.25, 11.5, 13.75 18. an  n 2  5n  2 19. 1075
20. 11,660
21. 364
22. 1806
23. r  3, a7  5832
24. 312.5
25. 2
26. an  2.3(2) n 1 27. 6, 18, 54, 162 28. 1.84351 29. -336.99
30. 3 31. no sum ( r  1)
32. 20
33. a)122 seats b) 1872
34. a) $41,250 b) $1,087,500
35. a) $33,700
b) $414,113
36. 128,848
***Memorize these formulas or pay 3 points for each formula during Ch. 10 test!
Arithmetic :
a n  a1  (n  1)d
Sn  n2 (a 1  a n )
a n  a1  r n1
Geometric :
2
Quadratic model: an  an  bn  c
Sn 
a 1 (1  r n )
1 r
if  1  r  1
Infinite Geometric :
a
S  1
1 r