About Arithmetic Sequence Explicit Formula
The explicit arithmetic sequence formula can be used to locate any term in a specified arithmetic sequence. An arithmetic sequence is set of numbers in which any two consecutive numbers have the same difference
The first item in an arithmetic sequence of 2, 5, 8, 11,... is a = 2, & the common difference is d = 5 - 2 = 3.
The arithmetic sequence explicit formula for this series is an = a + (n - 1)d, or an = 2 + (n - 1)3 or an = 3n - 1.
The explicit arithmetic sequence formula (an = 3n - 1) can be used to calculate any term in the series without knowing the previous term
What Is Arithmetic Sequence Explicit Formula?
Using its initial term (a) and the common difference, the arithmetic sequence explicit formula is used to discover any term (nth term) of the arithmetic sequence, a1, a2, a3,..., an... (d). The nth term formula of arithmetic sequence is given by this formula. The explicit formula for arithmetic sequence is a = a + (n - 1)d.
an = a + (n-1)d
Derivation of Arithmetic Sequence Explicit Formula
The explicit formula for the arithmetic sequence is derived from the terms of the arithmetic sequence. It makes it simple to locate any term in the arithmetic sequence. a1, a2, a3,..., an is the arithmetic sequence. The first term is designated as 'a,' and we have a = a1, with d denoting the common difference. The usual difference formula is d = a2 - a1 = a3 - a2 The explicit formula of the arithmetic sequence is represented by the nth term of an arithmetic sequence.
Explicit Formula- an= a + (n - 1) d
where,
- an = nth term of an arithmetic sequence
- a = the 1st term of an arithmetic sequence
- d = common difference (the difference between 2 successive terms. i.e., d = an− an−1)
Example of Arithmetic Sequence Explicit Formula
-3, -6, -9, -12,... is an arithmetic sequence in which the difference between any term and its previous term is -3. This difference is called as the common difference and is represented by the letter d. a1 or a = -3 represents the first
term of an arithmetic sequence. The arithmetic series explicit formula is
a = a + (n - 1)d = -3 + (n - 1)(-3) = -3n + 3 - 3 = -3n, or a = -3n,
using the formula for the nth component.
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