3 6 arithmetic sequences as linear functions

Here, the “fixed number” is called the “ common difference” and is denoted by 'd' i.e., if the first term is a 1, then: the second term is a 1+ d, the third term is a 1+ d + d = a 1 + 2d, and the fourth term is a 1 + 2d + d= a 1+ 3d and so on. We know that an AP is a sequence where each term, except the first term, is obtained by adding a fixed number to its previous term. Common Difference of Arithmetic Progression: For example, in the sequence 6, 13, 20, 27, 34. First Term of Arithmetic Progression:Īs the name suggests, the first term of an AP is the first number of the progression. An AP generally is shown as follows: a 1, a 2, a 3. Thus, an arithmetic progression, in general, can be written as: Ĭommon Terms Used in Arithmetic Progressionįrom now on, we will abbreviate arithmetic progression as AP. d = 4 (the 'common difference' between terms).We can also notice that every term (except the first term) of this AP is obtained by adding 4 to its previous term. is an arithmetic progression as the differences between every two consecutive terms are the same (as 4). The first term of an arithmetic progression is usually denoted by 'a' or 'a 1'.įor example, 1, 5, 9, 13, 17, 21, 25, 29, 33. This fixed number is known as the common difference and is denoted by 'd'. In this progression, each term, except the first term, is obtained by adding a fixed number to its previous term. See (Figure).An arithmetic progression (AP) is a sequence of numbers where the differences between every two consecutive terms are the same. A recursive formula for an arithmetic sequence with common difference d is given by +dn.The terms of an arithmetic sequence can be found by beginning with the initial term and adding the common difference repeatedly.The common difference is the number added to any one term of an arithmetic sequence that generates the subsequent term.

The constant between two consecutive terms is called the common difference.An arithmetic sequence is a sequence where the difference between any two consecutive terms is a constant.In this section, we will consider specific kinds of sequences that will allow us to calculate depreciation, such as the truck’s value. The truck will be worth $21,600 after the first year $18,200 after two years $14,800 after three years $11,400 after four years and $8,000 at the end of five years. The loss in value of the truck will therefore be $17,000, which is $3,400 per year for five years. After five years, she estimates that she will be able to sell the truck for $8,000. One method of calculating depreciation is straight-line depreciation, in which the value of the asset decreases by the same amount each year.Īs an example, consider a woman who starts a small contracting business. This decrease in value is called depreciation. The book-value of these supplies decreases each year for tax purposes. Use an explicit formula for an arithmetic sequence.Ĭompanies often make large purchases, such as computers and vehicles, for business use.

Use a recursive formula for an arithmetic sequence.

Find the common difference for an arithmetic sequence.

3 6 arithmetic sequences as linear functions