Pre-AP PreCalculus
Name____________________
WS 13.1 Putting it all Together Sequences and Series
Class Period ________
Identify the following sequences as arithmetic, geometric, or neither.
1. -3,6,-12,24…
2. 4,8,12,16…
4. Write the first five terms of the sequence. an 
3. 1,1,2,3,5,8…
n2
n
5. Find the first six terms of the sequence. a1  5, an  2an1
6. Find an explicit rule for the nth term of the arithmetic sequence. 4, 10, 16, 22, …
7. Find an explicit rule for the nth term of the sequence. The second and fifth terms of a
geometric sequence are -16 and 1024, respectively.
8. Find a recursive rule for the nth term of the sequence. -5, -15, -45, -135, …
9. A certain species of tree grows an average of 4.5 cm per week. Write an explicit rule
for the sequence that represents the weekly height of this tree in centimeters if the
measurements begin when the tree is 4 meters tall.
10. Write the series using summation notation. -1 + 3 + 7 + 11 + … + 59
11. Find the sum of the first n terms of the sequence. 5, -4, -13, -22, …; n = 9
12. A collection of dimes is arranged in a triangular array with 15 coins in the base row,
14 in the next, 13 in the next, and so forth with 1 dime in the last row. Find the value
of the collection.
13. A pendulum bob swings 6.0 cm on its first oscillation. On each subsequent
1
oscillation the bob travels
of the previous distance. Find the total distance the
3
bob travels before coming to rest.
14. State whether each sequence is arithmetic, geometric, or neither, and find a
formula for t n in terms of n. the first 5 terms of each sequence
A. 10, 6, 2, -2, …
a) the common difference or ratio
d) a recursive rule for the nth term
b) an explicit rule for the nth term
e) the first 5 terms of each sequence
c) the 10th term
f) the sum of the first 18 terms
B. 3, 6, 9, 12, 15, …
a) the common difference or ratio
d) a recursive rule for the nth term
b) an explicit rule for the nth term
e) the first 5 terms of each sequence
c) the 12th term
f) the sum of the first 15 terms
C. -2, 6, -18, 54, …
a) the common difference or ratio
d) a recursive rule for the nth term
b) an explicit rule for the nth term
e) the first 5 terms of each sequence
c) the 8th term
f) the sum of the first 10 terms
D. 1, _2, 4, _8, 16, . . .
a) the common difference or ratio
d) a recursive rule for the nth term
b) an explicit rule for the nth term
e) the first 5 terms of each sequence
c) the 11th term
f) the sum of the first 13 terms
15. Find the sum of the first n terms of the following sequences
a) 1, 4, 7, 10, ... n = 7
b) 8, 4, 2, 1, ... n = 8
c) 30, 26, 22, 18, ... n = 9
.
16. The first row of seating in section J of the Athena Arena has 7 seats. In all, there
are 25 rows of seats in section J, each row containing two more seats than the
row preceding it. How many seats are in section J?
17. Pat designs a patio with a trapezoid shaped deck consisting of 16 rows of
congruent slate tiles. The numbers of tiles in the rows form an arithmetic
sequence. The first row contains 15 tiles and the last row contains 30 tiles. How
many tiles are used in the deck?