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Name _____________________________________ Date _____________________
Sequences and Series Quiz Review
Find the first 4 terms of the sequence and determine if it is arithmetic, geometric or
neither.
1. t n  n 
1
n
 2
2. t n  3  
 3
2 n 1
____, ____, ____, ____
____, ____, ____, ____
___________________
___________________
Find the formula for t n and sketch the graph of each arithmetic or geometric sequence.
3. 30, 26, 22, 18,…
4. 80, 20, 5, …
______________
________________
State whether the given sequence is arithmetic, geometric or neither. Find a formula for
the nth term of the sequence.
a a2 a3 a 4
, , ,
9 18 36 72
5. 11, 101, 1001, 10001 …
6.
_______________
_______________
_____________________
_____________________
7. Find t12 in an arithmetic sequence
8. How many terms are in the geometric
1 1
sequence  , ,..., 1 ?
32 16
for which t3  8 and t6  6
9. How many numbers between 436 and 1,288 are multiples of 5?
Find the 3rd, 4th and 5th terms in each recursive sequence.
10. t1  2 , t n  n  t n1
11. t1  7 , t 2  3 , t n  t n1  2t n2
______, _____, _____
______, _______, _______
12. Give a recursive definition for
the sequence 1, 3, 7, 13, 21, 31, … ____________________________________
Find the specified sum for each series. In some problems, you may need to notice what
type of sequence you are given, in others you are told.
13. In an arithmetic series with t1  3
and t10  39 , find S10 .
14.
15. In a geometric series with t3 = 24
8
And t 6  , find S 7 .
9
16. Find S n in 1 + 2 + 4 + 8 + … + t n .
-1 + 4 + 9 + 14 +… + 999
17. Find the sum of all the multiples of 2 and 3 between 1,000 and 1,500.
18. Find the sum of the series 1 – 3 + 5 – 7 + 9 – 11 + … + 1001.
Evaluate the limit. Give its numeric value, state that it is  or   or state that the limit
does not exist.
n2 1
n4
8n 2  12n
19. lim
20. lim 2
21. lim
n
n n 2
n  2 n  1
5n 2
  1 
22. lim log cos 
n
  n 
23. lim
n 
 1n1
n
2
24. lim 4   1
n
n
“Calculator” Problems
25. In a city with a population of 875,000 the annual birth rate is 1.5%, but 25,000
people move out each year due to a tough job market. How many years from now will
the population drop below 750,000?
26. When Mr. Moneybags reaches his retirement age of 65, he expects to have a
retirement account worth $850,000. One month after he retires, and every month
thereafter, he intends to withdraw $8,000 from the account. The balance will be invested
at 5% annual interest compounded monthly.
a) Let An represent the amount of money in the account after n months. Write a
recursive definition for An .
b) When will he have less than $150,000 in his account?
1
2
1
3
2
1
2
3
105
27. Find


 ... 
10 20 30
100