20 Questions
What is the formal definition of a sequence?
A sequence is a function whose domain is the set of integers greater than or equal to a particular integer.
What does the ellipsis symbol '...' represent in a sequence?
An instruction to continue the sequence indefinitely.
How are terms of a sequence usually denoted?
Using the notation 'an' to represent the image of an integer.
Which set is commonly used as the domain for defining sequences?
{0, 1, 2, 3, ...}
What is the purpose of an explicit formula for a sequence?
To provide a rule showing how one term depends on another.
What is the fourth term of the sequence defined by the formula a_n = 1 + (-1)^n ?
2
Which type of sequence alternates between the values 2 and 0?
Alternating sequence
What is the explicit formula for the sequence with initial terms 0, 1, -2, 3, -4, 5, ... ?
$a_n = (-1)^{n+1} n$
What is meant by an arithmetic sequence or arithmetic progression (A.P.)?
A sequence with a common difference between consecutive terms
What is the 20th term of the arithmetic sequence 3, 9, 15, 21, ...?
39
What is the purpose of using the capital Greek letter sigma (∑) in math?
To write a sum in shorthand notation
In summation notation, what does 'k' represent?
The index of the summation
What is the result of computing the summation: 2 + (-2) + 0?
0
What is the expanded form of the summation: ∑(i=1 to 3) (2i+1)?
(2+1) + (3+1) + (4+1)
What is the value of ∑(k=1 to 4) k, where 'k' varies from 1 to 4?
10
What is the nth term of the arithmetic sequence in the text?
2n
What is the sum of the first n terms of an arithmetic series in the text?
$rac{n}{2}(2a + (n-1)d)$
If a is the first term and d is the common difference of an arithmetic series, what is the nth term formula?
$an = a + (n - 1)d$
In the context of the provided text, what is considered an arithmetic series?
1, 3, 5, 7, ...
If a dummy variable was introduced for the summation in the text, what would be a suitable choice?
$j$
Learn about sequences in mathematics, which are lists of elements written in a row. Explore examples of different types of sequences and their formal definition. Enhance your knowledge of sequencing concepts.
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