sequence
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
natural number means whose straiting from 1, 2, ................................. and counting numbers starting from 0,1, 2, ..........................................
The numbers are: 1-sqrt(2), 1 and 1+sqrt(2) or approximately -0.414214, 1 and 2.414214
The four consecutive natural numbers whose sum is 214 are 52, 53, 54 and 55.
A sequence is a function ! whose domian is the set of natural numbers
yes it is a function because sequence defined as "a function whose domain is set of natural number"
true
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.
A mathematical sequence whose verb is equal is the definition for an equation. An equation is given in the form A is equal to B. An equation can contain numbers and variables.
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
natural number means whose straiting from 1, 2, ................................. and counting numbers starting from 0,1, 2, ..........................................
The numbers are: 1-sqrt(2), 1 and 1+sqrt(2) or approximately -0.414214, 1 and 2.414214
The four consecutive natural numbers whose sum is 214 are 52, 53, 54 and 55.
A group of numbers in order. Usually, when talking about sequences, people talk about infinite sequences: a sequence that never ends (it has a first number, a second number, and an Nth number for any N, with no last number). There's no restriction of what the numbers are - they can be anything, and don't have to follow any pattern. But in practice, if you want to talk about a specific sequence, you'd need some rule for calculating the numbers in it. For example, you could have the sequence whose Nth term is 1/N. Sometimes sequences are taken to start with a 0th term rather than a first term. This is a question of notation, and doesn't really change anything about how sequences work. You can also think of a sequence as a function from the natural numbers {1,2,3,...} or {0,1,2,3,...} to whatever the sequence is of (usually real numbers, or sometimes complex numbers). For this reason, sequences are also called arithmetical functions. The most common way to write the nth term of a sequence is an (for one sequence; if you need to talk about more sequences, you'd write bn or cn)
5 + 6 + 7 = 18 Consecutive numbers means numbers following one another in sequence.