Utilizing the arithmetic sequence explicit formula for the nth term, we arrive at the following calculation: an = a + (n – 1)d = -3 + (n – 1)(-3) = -3n + 3 – 3 = -3n. The first term of this arithmetic sequence, which can be represented as a1 or simply ‘a,’ is equal to -3. Here, the parameters are defined as follows:Īn: The nth term of the arithmetic sequence.Ī: The first term of the arithmetic sequence.ĭ: The common difference, which signifies the difference between each term and its preceding term (i.e., d = an – an-1).Īlso Check – Arc Length Formula Example of Arithmetic Sequence Explicit FormulaĪn illustrative example of an arithmetic sequence is provided by the sequence -3, -6, -9, -12, …, in which the common difference, often denoted as ‘d,’ is consistently -3. The nth term of the arithmetic sequence corresponds to the explicit formula, which can be expressed as follows: In an arithmetic sequence represented as a1, a2, a3, …, an, the initial term is denoted as ‘a,’ with a1 being equivalent to ‘a.’ Additionally, the common difference is symbolized as ‘d,’ and its formula is derived as follows: d = a2 – a1 = a3 – a2 = an – an-1. The arithmetic sequence explicit formula finds its roots in the terms of the arithmetic sequence, offering a convenient method for determining any specific term within the sequence. Derivation of Arithmetic Sequence Explicit Formula The formula itself is expressed as an = a + (n – 1)d, offering a straightforward means of calculating the nth term of an arithmetic sequence. It relies on two key parameters: the first term (a) and the common difference (d) that characterize the sequence. The arithmetic sequence explicit formula serves as a powerful tool for determining any term within an arithmetic sequence (a1, a2, a3, …, an, …). Let’s explore the arithmetic sequence explicit formula in more detail, including its derivation and examples, to understand its practical applications better.Īlso Check – Area Formulas What Is Arithmetic Sequence Explicit Formula? This formula is a valuable tool for calculating specific terms within the sequence. So, the explicit formula for this arithmetic sequence is an = 3n – 1. This formula allows us to find the nth term (an) of the sequence without needing to know the previous term. The arithmetic sequence explicit formula is given as: The common difference (d) is 3, which is calculated as 5 – 2 = 3. Let’s take an example: consider the arithmetic sequence 2, 5, 8, 11, …. This common difference is denoted as ‘d.’ An arithmetic sequence is a sequence of numbers where the difference between any two consecutive terms is constant. The arithmetic sequence explicit formula is a valuable tool for finding any term in a given arithmetic sequence.
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