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Is sequence a function?
yes it is a function because sequence defined as "a function whose domain is set of natural number"
A sequence is a whose domain is the set of natural numbers?
true
Why the graph of a sequence cannot be a line or a curve?
A sequence can be thought of a list of numbers written in a definite order:a1, a2, a3, ..., a(n+1), an, ...The number a1 is called the first term, a2 is the second term, and in general an is the nth term.For every positive integer n, there is a corresponding number an, and so a sequence can be defined as a function whose domain is the set of all positive integers. But, we usually write an instead of the function f(n) for the value of the function at the number n.Notation: The sequence {a1, a2, a3, ...} is also denoted by {an}.Some sequences can be defined by giving a formula for the nth term. For example:an = (n)/(n +1) the sequence is {1/2, 2/3, 3/4, 4/5, ..., (n)/(n+1), ...}this sequence can be pictured either by plotting its terms on a number line, or by plotting its graph. Since a sequence is a function whose domain is the set of positive integers, its graph consists of isolated points with coordinates (1, a1), (2, a2), (3, a3), ..., (n, an).Try to plot the graph of this sequence, and you will see that the terms of the sequence an = n/(n+1) are approaching 1 as n becomes large. In this case 1 is the limit for this sequence, and we can write:lim n -->∞ an = 1
Could this ever be the rule of a function For input x the output is the number whose square is x If so what is its domain and range?
Yes, the domain(input) would be all natural numbers (numbers greater or equal to zero). The range (output) would be all real numbers. -- Not only natural numbers would be considered part of this domain, all negative numbers are also reasonable inputs to this function, as any negative number multiplied by itself would produce a positive number..... The output (range) would therefore be all positive real numbers......
A mathematical sequence whose verb is equal?
formula
Is sequence a function?
yes it is a function because sequence defined as "a function whose domain is set of natural number"
A sequence is a whose domain is the set of natural numbers?
true
What is the function whose domain is a set of consecutive integers there are finite and infinite?
sequence
What is an sequence?
A sequence is a list whose members each have the same relationship to the member that precedes it in the list. For example, in the sequence 2, 3, 5, 9, 17, each number after 2 is one less than double its predecessor. Alternatively, a sequence is simply an infinite list of numbers, or a function with the positive integers as the domain.
What is a sequence whose terms differ by the same nonzero number d called thecommon difference?
An arithmetic sequence.
What is the nth term of sequence 392781243...?
The question does not contain a sequence but a single large number whose digits are the digits of the sequence, 3n run together. There is only one number, not a sequence, so there is no nth term.
What is a sequence whose successive terms differ by the same nonzero number d called the common difference?
It's technically called an arithmetic sequence
Why the graph of a sequence cannot be a line or a curve?
A sequence can be thought of a list of numbers written in a definite order:a1, a2, a3, ..., a(n+1), an, ...The number a1 is called the first term, a2 is the second term, and in general an is the nth term.For every positive integer n, there is a corresponding number an, and so a sequence can be defined as a function whose domain is the set of all positive integers. But, we usually write an instead of the function f(n) for the value of the function at the number n.Notation: The sequence {a1, a2, a3, ...} is also denoted by {an}.Some sequences can be defined by giving a formula for the nth term. For example:an = (n)/(n +1) the sequence is {1/2, 2/3, 3/4, 4/5, ..., (n)/(n+1), ...}this sequence can be pictured either by plotting its terms on a number line, or by plotting its graph. Since a sequence is a function whose domain is the set of positive integers, its graph consists of isolated points with coordinates (1, a1), (2, a2), (3, a3), ..., (n, an).Try to plot the graph of this sequence, and you will see that the terms of the sequence an = n/(n+1) are approaching 1 as n becomes large. In this case 1 is the limit for this sequence, and we can write:lim n -->∞ an = 1
Could this ever be the rule of a function For input x the output is the number whose square is x If so what is its domain and range?
Yes, the domain(input) would be all natural numbers (numbers greater or equal to zero). The range (output) would be all real numbers. -- Not only natural numbers would be considered part of this domain, all negative numbers are also reasonable inputs to this function, as any negative number multiplied by itself would produce a positive number..... The output (range) would therefore be all positive real numbers......
Does there exists any sequence whose limit is positive but sequence is negative?
No, such a sequence is not posible.
What is the difference between a sequence and a series?
The sum of the terms in a sequence is called a series. Sequence is a function whose domain is the natural numbers. So f(1)= first entry in the sequence, and f(2) is the next.... f(n) is the nth term. We usually don't write sequences that way. Instead of f(1) we write, a1 to refer to the first term. The function tells us the rule we use to find the terms of the sequence. So for example, f says take n and square it. Then the first 3 terms of the sequence are 1, 4 and 9 and the first 3 terms of the series are 1, 5 and 14
Is a series a function whose domain is the set of real number?
Not necessarily. There are series over all kinds of subsets and supersets of the set of real numbers.
