Sequence and Series Worksheet #2 Date:______ 1) Determine i

Advanced Algebra II
Sequence and Series Worksheet #2
Name:_________________________Per:______
Date:__________
1) Determine if the following sequences are arithmetic, geometric, or other. For the arithmetic and geometric
sequences, find .
a) 5, 7, 9, 11, … b) 5, 15, 45, ….
c) 9, 12, 16, 21, … d) -4, 24, -144, …
e) -19, 16, 51, … f) 32, 16, 8, 4 ….
2) The finite sequence 5, 7, 9, 11 can be written as a finite series as 5 + 7 + 9 + 11. The sum of this finite
series is 32. Rewrite the finite sequence 5, 15, 45, 135, 405 as a finite series and then find its sum.
3) The infinite sequence 3, 7, 11, 15, … can be written as an infinite series as
3 + 7 + 11 + 15 + … .
a) Rewrite the infinite sequence 6, 13, 20, 27, … as an infinite series. What would be the sum of that
infinite series?
b) Rewrite the infinite sequence 17, 6, -5, -16, -27, … as an infinite series. What would be the sum of that
infinite series?
4) Find the sum of the first 50 natural numbers.
5) Find the sum of the first 200 terms in the series 5 + 7 + 9 + 11 + … .

6) Seven years ago Raj found a box of old baseball cards in the garage. Since then he has added a consistent
number of cards to the collection each year. He had 52 cards in the collection after 3 years and now he has
108 cards.
a) What type of sequence are we dealing with? Why? What is the general equation for this type of
sequence?
b) Let n be the time and be the number of cards he has. Write two algebraic equations. Solve your two
equations (hint: you should be solving for the variables “d” and “c”) to determine the number of cards in
his collection after n years (i.e. find ).
c) How many cards were in the box that Raj found?
d) How many cards is Raj adding to his collection each year?
e) Raj plans to keep the collection for a long time. How many cards will the collection contain 10 years
from now?
7) The track coach decided to have his athletes run three laps the first day of practice for their warm-up. He
increased the total number of laps they would run each day by two. If track season is 55 days longs, how
many laps:
a) did the athletes run for warm-ups on day 20?
b) did the athletes run for warm-ups on day 55?
c) did they run for warm-ups during the entire season?

8) Consider the finite arithmetic series 10 + 13 + 16 + … + 31.
a) How many terms are in the series?
b) Evaluate the series (i.e. find the sum).
9) Solve each for x
a) 9x² - 17 = 3 b)
4x
−
3
1
2 x
=
23
6
c)
x − 3
=
6
x + 8
− 2
10) Find the domain and range of each graph.
a) b)

11) Consider the sequence 3, 18, …
a) Assuming the sequence is arithmetic:
i) find the 12 th term.
b) Assuming the sequence is geometric:
i) find the 7 th term.
ii) Is 203 in the sequence? Explain your
answer.
ii) Is 648 in the sequence? Explain your
answer.
iii) Find the sum of the first 80 terms.
iii) Is 23,320 in the sequence? Explain your
answer.
12) An arithmetic sequence contains the following terms: = -47 and = 13. Find algebraically.
13) Factor completely.
a) 32x 3 − 18x
b) 24x
2 −11x
−18
c) 8 10 12 15 d)
3 3
27x − 8y
To complete this assignment do BB 49-52, 61,63 on a separate sheet of paper.