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The arithmetic sequence explicit formula can be easily computed from the term of the sequence. What is Explicit Formula For Arithmetic Sequence? Similarly, the explicit formula can be computed for the geometric sequence and harmonic sequence. And the explicit formula for this arithmetic sequence is a n = a + (n - 1)d. a + (n - 1)d, the n th term forms the explicit formula of the sequence. For the arithmetic progression, a, a + d, a + 2d, a + 3d. The explicit formula can be written from the n th term of the sequence. The explicit formula for the arithmetic sequence is a n = a + (n - 1)d, for the geometric sequence is a n = ar n-1, and for the harmonic sequence is a n = ar n-1. The n th term of the sequence forms the explicit formula and any term can be computed by substituting the value of n in the explicit formula. The explicit formula is useful to find any term of the sequence without the help of the previous terms of the sequence. is a n = n 2 as every term is a square number of its position.įAQs on Explicit Formula What is Explicit Formula In Algebra? For example, the explicit formula for the sequence 1, 4, 9, 16, 25. Apart from, the explicit formulas of arithmetic, geometric, and harmonic sequences, there can be any other formulas.To write the explicit formula, there should be a pattern that all terms follow.Any set of terms cannot be expressed by explicit formula.Thus the harmonic sequence explicit formula for this sequence is a n = 1/(3n - 1). the value of a = 2, and d = 5 - 2 = 3, and the nth term of the sequence is 1/(2 + (n - 1)3) = 1/(3n - 1). This explicit formula of the harmonic sequence helps to easily find any term of the sequence, without knowing the previous terms. Here 1/(a + (n - 1)d) is the general term of the harmonic sequence and is the required explicit formula.Įxplicit formula for finding the n th term of harmonic sequence: a n = 1/(a + (n - 1)d)

The terms of the harmonic sequence are 1/a, 1/(a + d), 1/(a + 2d), 1/(a + 3d). The harmonic sequence explicit formula is useful to easily find any term of the harmonic sequence without finding the other terms of the sequence. The explicit formula is also helpful to represent the entire sequence with a single formula. Generally, the n th term of the sequence represents the explicit formula. ) which can be uniquely represented using an explicit formula (a n = 2n). Let us consider a simple sequence of even numbers(2, 4, 6, 8. The above explicit formulas are helpful to find any term of the arithmetic sequence, geometric sequence, or harmonic sequence, by simply substituting the n values in the respective explicit formulas.

Harmonic Sequence: a n = 1 /, where 'a' is the first term and 'd' is the common difference of the arithmetic sequence formed by taking the reciprocals of the harmonic sequence.

Geometric Sequence: a n = a r n - 1, where 'a' is the first term and 'r' is the common ratio.

Arithmetic Sequence: a n = a + (n - 1) d, where 'a' is the first term and 'd' is the common difference.

Here are the explicit formulas of different sequences: The explicit formula helps to easily find any term of the sequence, without knowing its previous term. The terms of a sequence can be uniquely represented using a single formula, which is the explicit formula. The meaning of "explicit" is direct, something that can be directly found without knowing the other terms of the sequence. Here, the n th term is representative of the explicit formula of the arithmetic sequence.Explicit formulas are always used to represent any term of the sequence, without writing the other terms of the sequence. The common difference is 'd' which is the difference between any two adjacent terms of the sequence. Here, the first term which is generally referred to as 'a' is a1. Let us assume the arithmetic sequence is a 1, a 2, a 3, a 4, a 5.,a n. The video below explains this: Arithmetic Progression Detailed Video Explanation:ĭerivation of Arithmetic Sequence FormulaĪrithmetic sequence formula can be derived from the terms present in the arithmetic sequence itself. The arithmetic sequence explicit formula can be mathematically written as This formula will help us to reach the nth term of the sequence.

Arithmetic sequence explicit formula allows us to find any term of an arithmetic sequence, a 1, a 2, a 3, a 4, a 5., a n using its first term (a 1) and the common difference (d).