Define arithmetic sequence.
A sequence of numbers in which the difference between consecutive terms is constant.
What is the common difference in an arithmetic sequence?
The constant amount added to each term to get the next term.
True or false: An arithmetic sequence can have a negative common difference.
TRUE
This results in a decreasing sequence.
Fill in the blank: The n-th term of an arithmetic sequence is given by _______.
a_n = a_1 + (n-1)d
What is the first term of the sequence 5, 8, 11?
5
Find the common difference for the sequence 3, 7, 11.
4
True or false: The sequence 10, 10, 10 is an arithmetic sequence.
TRUE
The common difference is 0.
What is the 10th term of the sequence 2, 5, 8?
29
Define arithmetic series.
The sum of the terms of an arithmetic sequence.
Fill in the blank: The sum of the first n terms of an arithmetic series is _______.
S_n = n/2 * (a_1 + a_n)
What is the sum of the first 5 terms of the sequence 1, 4, 7?
50
True or false: An arithmetic sequence can have non-integer terms.
TRUE
Examples include sequences like 1.5, 2.5, 3.5.
What is the common difference in the sequence 12, 9, 6?
-3
Fill in the blank: The sequence 4, 10, 16 is an arithmetic sequence with a common difference of _______.
6
What is the formula for the n-th term of an arithmetic sequence?
a_n = a_1 + (n-1)d
What is the first term of the sequence 15, 20, 25?
15
True or false: The sequence 1, 3, 5, 7 is an arithmetic sequence.
TRUE
The common difference is 2.
Define convergent arithmetic sequence.
An arithmetic sequence that approaches a limit as n increases.
What is the last term of the sequence 2, 5, 8, …, 20?
20
Fill in the blank: The n-th term of an arithmetic sequence can also be expressed as _______.
a_n = a_1 + (n-1)d
What is the sum of the first 10 terms of the sequence 1, 2, 3?
55
What is the common difference in the sequence 100, 95, 90?
-5
True or false: The sequence 7, 14, 21 is an arithmetic sequence.
TRUE
The common difference is 7.
What is the first term of the sequence 0, 1, 2?
0
