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What is the explicit rule for the arithmetic sequence shown in the graph?

What is the explicit rule for the arithmetic sequence shown in the graph?

Graph an arithmetic sequence and geometric sequence

Significant acquisitions, such as computers and cars, are often made for commercial purposes. For tax purposes, the book value of these supplies falls per year. Depreciation is the term for this reduction in value. Straight-line depreciation is a method of estimating depreciation in which the asset’s value decreases by the same amount each year.
Since the values of the truck in the example shift by a constant amount each year, they are said to form an integer series. Each term increases or decreases by the same constant value known as the sequence’s common difference. The average difference in this series is -3,400.
Arithmetic sequences have the property that the difference between any two consecutive terms is always the same. The popular difference is the name given to this constant. If (a 1) is the first term of an arithmetic sequence and (d) is the typical difference, the sequence will be: Figure (PageIndex1) shows the graph of each of these sequences. Although both sequences show progression, we can see from the graphs that (a) is not linear while (b) is. Since the rate of change in arithmetic sequences is constant, their graphs will always be points on a line.

Al2 arithmetic sequences given two terms algebra 2 common

The first quadrant is used to graph this series. Remember that the domain is made up of natural numbers like 1, 2, 3, and so on, while the spectrum is made up of sequence names. It’s worth noting that this series appears to be linear. “5 over 1” is the rate of change between each of the points. The n value increases by a constant of one, while the f (n) value increases by a constant of five (for this graph).
It’s worth noting that this series appears to be exponential. With geometric sequences, it’s possible that the graph will develop (or decrease). As the value of n increases, the rate of change will increase (or decrease) (it is not constant).
It will be much easier to see the trend for an explicit formula for an arithmetic or geometric sequence than it will be to find explicit formulas for sequences that do not fall into these categories.
The Fibonacci series, as seen in this illustration, is a well-known sequence. [Leonardo Fibonacci introduced it in 1202]. The sequence’s first term was 1 in its original form. The sequence can now begin with either 1 or 0.] [According to modern convention, the sequence can now begin with either 1 or 0.]

Writing explicit functions given the graph

A continuous function in mathematics is one for which small changes in the input result in arbitrarily small changes in the output. A function is said to be discontinuous if it is not otherwise.
A continuous function in mathematics is one for which small changes in the input result in arbitrarily small changes in the output. A function is said to be discontinuous if it is not otherwise.
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Learn how to find the 40th term or an arithmetic sequence

A recursive formula is used to describe certain arithmetic sequences in terms of the previous definition. The formula establishes an algebraic law for deciding the sequence’s names. Using a function of the preceding term, we can find any term of an arithmetic sequence using a recursive formula. Each term is calculated by adding the previous term and the common difference. If the common difference is 5, for example, each term is equal to the previous term plus 5. The first word, as with any recursive formula, must be defined.