The common difference may be positive or negative. In an arithmetic sequence, each term after the first is obtained by adding a constant, or common difference, to the preceding term. Where u is the nth term and n is any positive integer. If we know the first term (a1) and the common difference (d) of an arithmetic sequence, we can find the nth term using the following formula: Thus, the first few terms of an arithmetic sequence may be written as: The common difference between successive terms of an arithmetic sequence is denoted by d. Nth Term of Arithmetic SequenceĪn arithmetic sequence is a sequence in which each term after the first is obtained by adding a constant to the preceding term. N represents the position of the term in the sequence. The nth term of an arithmetic sequence is given by the formula: The constant d is called the common difference. Arithmetic Sequence FormulaĪn arithmetic sequence is a list of numbers in which each number after the first is obtained by adding a constant, d, to the preceding number. For example, the list 2, 4, 6, 8 … is NOT an arithmetic sequence because each successive number is not equal to the previous number plus a constant (in this case, 2). It’s important to note that not all lists of numbers are arithmetic sequences. So we could say that in our example above, a_5=7 because it is the 5th term in our list and its value is 7. Notice that in this equation, n represents the position of the term in the sequence and not its value. Where a_n represents the nth term of the sequence, a_1 represents the first term of the sequence, and d represents the common difference. In general, an arithmetic sequence can be represented by the following equation: For example, the list 1, 3, 5, 7, 9 … is an arithmetic sequence because each successive number is the previous number plus 2. The constant is also called the common difference. Examples of Arithmetic SequencesĪn arithmetic sequence is defined as a list of numbers in which each successive number is the previous number plus a constant. Where d is the common difference and n is the position of the term in the sequence. Where a_1 is the first term and a_n is the nth term. The arithmetic mean or average of an arithmetic sequence is given by: The first number of an arithmetic sequence is called the first term and the last number is called the last term. The common difference may be positive, negative, or zero. Definition of Arithmetic SequenceĪn arithmetic sequence is a sequence of numbers in which each successive number is obtained by adding a fixed number, called the common difference, to the preceding number. Where d is the common difference and a is the first term in the sequence. The general form of an arithmetic sequence is: For example, the sequence 3, 5, 7, 9, 11,… is an arithmetic sequence because each successive number is the previous number plus 2. The constant is called the common difference. Using this information we can write out the first few terms of this sequence:Ī1=3 a2=a1+d=3+2=5 a3=a2+d=5+2=7 a4=a3+d=7+2=9… Arithmetic SequenceĪn arithmetic sequence is a list of numbers in which each successive number is the previous number plus a constant. The first term in this sequence is 3 and the common difference is 2. For example, consider the following arithmetic sequence: Where a1 is the first term in the sequence and d is the common difference between successive terms. So, the general form of an arithmetic sequence is: In an arithmetic sequence, each term after the first is obtained by adding a constant, d, to the preceding term. Where a1 is the first term and d is the common difference. To find the nth term of an arithmetic sequence we use the formula: So, using our example above, we would say that a1 = 3 and d = 2. The first number in an arithmetic sequence is called the first term and the common difference is often denoted by d. For example, the sequence 3, 5, 7, 9, 11, 13,… is an arithmetic sequence because each successive number is the previous number plus 2. The initial term (a) of an AP may be any number each subsequent term (an) is obtained by adding the common difference d to the previous term: a_n=a_(n-1)+d The nth term of an AP is given by a_n=a+d(n-1) What is an Arithmetic Sequence?Īn arithmetic sequence is a list of numbers in which each successive number is the previous number plus a constant. An arithmetic progression (AP) or arithmetic sequence is a mathematical series in which each term after the first is obtained by adding a constant to the preceding term. For example, the sequence 1, 3, 5, 7, 9, … is an arithmetic sequence with common difference of 2. In mathematics, an arithmetic sequence is a sequence of numbers such that the difference between any two consecutive members of the sequence is a constant. Arithmetic Sequence Definitions and Examples
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