Arithmetic Sequence

An Arithmetic Sequence is a formally defined number sequence define in terms of arithmetic operations on the earlier sequence member.

• AKA: Arithmetic Progression.
  • …
• Example(s):
  • n' = n²
  • n' = (n-1)+(n-2)
  • αn = α1 + (n-1)d
• See: string, Formal Number Sequence, Fibonacci Sequence.

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References

2013

• http://en.wikipedia.org/wiki/Arithmetic_progression
  • In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

    For instance, the sequence 5, 7, 9, 11, 13, 15 … is an arithmetic progression with common difference of 2.

    If the initial term of an arithmetic progression is [math]\displaystyle{ a_1 }[/math] and the common difference of successive members is d, then the nth term of the sequence ([math]\displaystyle{ a_n }[/math]) is given by: :[math]\displaystyle{ \ a_n = a_1 + (n - 1)d, }[/math] and in general :[math]\displaystyle{ \ a_n = a_m + (n - m)d. }[/math] A finite portion of an arithmetic progression is called a finite arithmetic progression and sometimes just called an arithmetic progression. The sum of a finite arithmetic progression is called an arithmetic series.

    The behavior of the arithmetic progression depends on the common difference d. If the common difference is:

  • Positive, the members (terms) will grow towards positive infinity.
  • Negative, the members (terms) will grow towards negative infinity.

2009

• http://www.sparknotes.com/testprep/books/sat2/math2c/chapter12section2.rhtml
  • An arithmetic sequence is an ordered list of terms in which the difference between consecutive terms is constant. In other words, the same value or variable is added to each term in order to create the next term: if you subtract any two consecutive terms of the sequence, you will get the same difference. An example is {αn} = 1, 4, 7, 10, 13, . . ., where 3 is the constant increment between values. The notation of an arithmetic sequence is: αn=α1+(n-1)d

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