Arithmetic Sequences
The fixed number combined with a term within an arithmetic sequence to establish the next term in the sequence. It is the difference between each pair of consecutive terms in the sequence.
Common Difference
The fixed number used to multiply terms in geometric sequence to determine the next term in the sequence
Common Ratio
Define a "Triangular number"
A sequence of numbers representing the sum of consecutive integers, starting from 1 that can be visualized as dots arranged in the shape of an equilateral triangle
Define: Conjecture
A statement that is believed to be true but has not yet been proven
Determine the common difference in this arithmetic sequence:
10, 7, 4, 1 ...
-3
What is the next term in the geometric sequence?
16, 64, 256, 1,024, ____, ...
4,096
Define "Term"
Any given number within a sequence
Define: Counterexample
A specific example that disproves a statement, showing it is not universally true
Identify the missing term in the arethmetic sequence:
12, ___, 26, 33, 39
19
Identify the missing term:
4, 12, ___, 108
36
Which mathematical principle can the following formula be used?
an=a1+(n-1)d
Arithmetic Sequences
True or False: If false, provide a counterexample.
The product of any two even numbers is always an even number.
True
Identify the 18th term in this arithmetic sequence:
100, 85, 70, 55, ...
a18 = -155
A scientist is observing a bacterial culture that starts with 50 bacteria. The number of bacteria doubles every hour. How many bacteria will there be after 3 hours?
400 Bacteria
Which mathematical principle can the following formula be used?
an = a1 x r(n-1)
Geometric Sequences
True or False: If false, provide a counterexample.
Subtracting a positive number from another positive number always results in a positive number.
False
8 - 12 = -4
Identify the 37th term in the arithmetic sequence:
4, 10, 16, 22, ...
a37 = 220
Marco is saving money for a new bike. He starts with $25 in his savings jar. Each week, he adds $8. How much total money will he have in the jar at the end of week 5?
$65
Identify the two major differences between an arithmetic sequence and a geometric sequence.
An arithmetic sequence uses a common difference to add to the previous term to obtain the next.
A geometric sequence uses a common ratio to multiply the previous term to obtain the next.
True or False: If false, provide a counterexample.
The product of an even number and an odd number is always odd.
False
4 x 3 = 12 (even)