Arithmetic Sequences
What is the common difference of the sequence?
4, 9, 14, 19, ...
5
What is the common ratio?
3, 6, 12, 24, ...
r = 2
A gym charges a $25 sign-up fee plus $15 per month. Write an equation for the total cost after n months, including the sign-up fee. Is the sequence of monthly total costs arithmetic or geometric?
Arithmetic
The total cost after n months is an=25+15n. The monthly costs form an arithmetic sequence with common difference $15.
Evaluate 5!
120
Find the next two terms.
23, 17, 11, 5, ...
-1 and -7
Find the next two terms.
160, 80, 40, 20, ...
10, 5
A bacteria population starts at 200 and doubles every hour. Write an equation for the population after n hours.
Geometric
P(n)=200(2)n-1
Evaluate 6!/4!
30
An arithmetic sequence has a first term of 7 and a common difference of 4. What is the 12th term?
51
A geometric sequence starts at 5 and has a common ratio of 3. Find the 6th term.
a6=5(35)=1,215
A theater has 20 seats in the first row, 24 in the second row, 28 in the third row, and so on. Write an explicit equation for the number of seats in row n. Identify the type of sequence.
Arithmetic
an=20+4(n-1)
Expand 7! as a product of whole numbers.
7 * 6 * 5 * 4 * 3 * 2 * 1
The 4th term of an arithmetic sequence is 18, and the 10th term is 42. Find the first term and the common difference.
d = 4, a1 = 6
A geometric sequence has a first term of 4 and a fourth term of 108. Find the common ratio, assuming it is positive.
108=4r3, so r=3
A car is worth $30,000 when purchased and loses 12% of its value each year. Write an equation for its value after n years. Identify the type of sequence.
Geometric
V(n)=30,000(0.88)n
Simplify 8! / 6! * 2!
28
The 5th term of an arithmetic sequence is 21, and the 13th term is 53. Which term has a value of 81?
a1=5, d=4; an=5+4(n-1). The 20th term is 81.
The first term of a geometric sequence is 192, and the common ratio is 12. Which term is the first term less than 2?
The 8th term is 192(12)7=1.5, so the 8th term is the first term less than 2.
A student begins saving $50. Each week, the student saves 1.5 times as much as the previous week. The first week's deposit is $50. Write an explicit equation for the amount saved in week n, and identify the type of sequence.
Geometric
an=50(1.5)n-1
Expand 12! / 6!
(12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)/
6 * 5 * 4 * 3 * 2 * 1