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. Explicit formulas are always used to represent any term of the sequence, without writing the other terms of the sequence.
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