Final Review: Sequences & Series Unit
Name:
Pd:
Answer all questions on your own paper, using graph paper where necessary.
1) Find the sums:
5
a)
2
c)  3 
i 1  3 
 i 2  2i
6
i 0
50
b)
  2i  14

d)
i 1
i
 5
 

2
i 1 
i 1
2) Determine whether the sequence is arithmetic, geometric, or neither, and write an explicit rule
for each sequence.
a) 517, 501, 485, 469, …
c) 3, -9, 27, -81, …
b) 1, 4, 9, 16, …
d) 4928, 2464, 1232, 616, …
3) Write a recursive rule for the sequence: 2, 4, 6, 10, 16, 26, ….
4) Write an explicit rule for the arithmetic sequence with a 6  13 and a14  25 . Find the 10th
term of the sequence.
5) Write an explicit rule for the geometric sequence with a3  25 and a 6  
25
. Find the 8th
64
term of the sequence.
6) In the geometric sequence with a2  14 and a4  350 , what term is 218750?
7) Find the explicit rule for the sequence 10, 12.5, 15, 17.5, … , determine whether it is arithmetic,
geometric, or neither, and find its 20th partial sum.
8)
Find the explicit rule for the sequence 2, 6, 18, 54, … , determine whether it is arithmetic,
geometric, or neither, and find its 12th partial sum.
9) Find the explicit rule for the sequence 352, 88, 22,
11
, ... , determine whether it is arithmetic,
2
geometric, or neither, and find its infinite series sum.
10) Rewrite the decimal 2.373737373737… as a fraction.
11) Find the 12th term of the sequence with the recursive rule an  2an1  5 if a10  133 .
12) If 6, 18, 38, 68, 110, and 164 are the first 6 partial sums of the sequence a n  n 2  3n  2 , find
a polynomial formula that will give you the nth partial sum.
x
13) Solve for x:
3
 10  4
i 1
 26214.3
i 1
14) A tiled area in front of a fireplace is in the shape of a trapezoid. The first row of tiles uses 20
tiles, the second row uses 22, the third row uses 24, and so on.
a) If there are 40 tiles in the last row, how many rows are there in the tiled area?
b) How many tiles were used in total?
15) The crew of a ship accidentally left their four pet rabbits on an island with no predators. The
population of rabbits will double every month.
a) How many rabbits will there be when the ship comes back in six months?
b) How much time will it take before the population of rabbits is over nine thousand?
16) Consider the following figure:
If the shading process continues indefinitely, how much of the area of the original square will
eventually be shaded?