What is an arithmetic series? Calculating geometric and arithmetic sequences Series
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lernflix.at offers individual online tutoring in mathematics. For more information go to https://lernflix.at/ In mathematics, a sequence is a list (family) of a finite or infinite number of consecutively numbered objects (for example numbers). The same object can appear multiple times in a sequence. An arithmetic sequence (also: arithmetic progression) is a regular mathematical sequence of numbers with the property that the difference between two adjacent sequence terms is constant. A simple arithmetic sequence is represented by the odd natural numbers: 1,3,5,7,9,... The two most important sequences are the arithmetic and the geometric sequence. They occur in nature (radioactive decay, bacterial growth), finance (interest and compound interest) and many other areas. You can also see that switching between explicit and recursive representation is very easy. You can see that the similarity of the two definitions is not accidental; the arithmetic sequence grows additively, the geometric sequence grows multiplicatively. The geometric sequence occurs in many growth and decay processes in nature; both arithmetic and geometric sequences have their place in interest calculations. A geometric sequence is a regular mathematical sequence of numbers with the property that the quotient of two neighboring terms of a sequence is constant. The term "geometric sequence" is derived from the geometric mean. Each term of a geometric sequence is the geometric mean of its neighboring terms. The summation of the terms of the sequence results in the geometric series. A geometric series is the series of a geometric sequence whose nth term is the sum of the first n terms of the corresponding geometric sequence. We differentiate between finite and infinite series, depending on whether n is finite or not. An infinite geometric series arises when n in the geometric series approaches infinity. Arithmetic series are special mathematical series. An arithmetic series is the sequence whose terms are the sum of the first n terms (the partial sums) of an arithmetic sequence. Arithmetic series are generally divergent. Therefore, we are particularly interested in partial sums, which are also known as finite arithmetic series. There is a simple formula for calculating partial sums or finite arithmetic series. The sum of a finite arithmetic sequence is the number of terms multiplied by the arithmetic mean of the first and last terms. Mathematics tutoring in Villach
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