Review of All Sequences and Series
Name_________________________
1.
One characteristic has been given about four different infinite geometric series. Based
on the characteristic, circle every sequence that would have a sum if one wanted to
add all of the terms in the series.
Sequence 1 - has a common ratio of 10
1
Sequence 2 - has a common ratio of
2
Sequence 3 - has a common ratio of -0.99
5
Sequence 4 - has a common ratio of 
3
------------------------------------------------------------------------------------------------------------------------------2.
In a geometric sequence, suppose a4  2 and a7  85.75 . What is a9 ?
41
3.
Evaluate:
  9n  35 .
n 8
4.
How many terms are in the finite geometric sequence below?
5, 20, 80, ... , 327680, 1310720, 5242880
5.
Find the sum of the 1st 13 terms of a geometric series that has an explicit formula
of an  125  (2)n1 .
6.
Suppose an arithmetic sequence is constructed in which the value of the 8th term
is 1059, and the value of the 56th term is 1731. What is the explicit formula
for this sequence?
7.
An arithmetic sequence has an explicit formula of an  n  5 . What is the value
of the 15th term of the sequence?
8.
Consider the geometric series: 1 + 3 + 9 + 27 + ...
The sum of the 1st n terms of the geometric series is 21523360. What is the value
of n?
9.
Find the value of n in the following expression:
n
 8k  6  65,280 .
k 1
10.
A geometric sequence has a common ratio of -9, and a 2nd term with a value of 7.2.
What is the position (1st, 2nd, 3rd, etc.) of the term with a value of -34437376.8?
11.
Find the sum of all of the terms from the 16th thru the 71st term for the series
given below:
(-500) + (-480) + (-460) + (-440) + ...
12.
Evaluate:

2
 900  (3)
n 1
.
n 1
6
13.
Evaluate:
n
3
 5n .
n 3
14.
Suppose the sum of the 1st n terms of series is 53700. If the explicit formula for the
series is an  6n  811 , what is the value of n?
15.
Evaluate:
10
  10.125  (4)
n 1
.
n5
16.
What is the position of the term with a value of 1,953,125 in the sequence with an
explicit formula of an  0.2  (5)n1 ?
17.
Consider the explicit formula an  ________ .
A)What type of expression (in terms of n) must be in the blank in order for the formula
to correspond to an arithmetic sequence?
B)What type of expression (in terms of n) must be in the blank in order for the formula
to correspond to an geometric sequence?
18.
What is the sum of all of the terms in this series: 1600 + (-1200) + 900 + (-675) + ...?
Round to the nearest tenth.
19.
What is the sum of all of the terms in the finite geometric series below?
11 + 22 + 44 + ... + 11264 + 22528 + 45056
20.
An arithmetic sequence is constructed such that a22  35 , and a49  278 .
What is a1 ?
------------------------------------------------------------------------------------------------------------------------------1. Sequence 1 and 4 2. -1050.4375 3. -6307 4. 11 5. 1,023,875 6. an  14n  947
7. -20 8. 16
15. 2,122,848
9. 128 10. 9th 11. 19,600 12. 2700 13. 342 14. 150
16. 11th 17. A)linear B)exponential 18. 914.3 19. 90101
20. 154