We can get any term in the sequence by taking the first term 5 and adding the common difference 3 to it repeatedly. In order to find the fifth term, for example, we need to plug n=5 into the explicit formula.Ĭool! This is in fact the fifth term of 3, 5, 7,… Writing explicit formulasĬonsider the arithmetic sequence 5,8,11,…The first term of the sequence is 3 This formula allows us to simply plug in the number of the term we are interested in, and we will get the value of that term. In the formula, n is any term number and a(n) is the n th term. Here is an explicit formula of the sequence 3, 5, 7,… Then, the sum of the first n terms of an arithmetic sequence is S n = na 1 + n/ 2( dn – d ). To use the second method, you must know the value of the first term a 1 and the common difference d. Then, the sum of the first n terms of the arithmetic sequence is S n = n( a 1+a n/ 2). To use the first method, you must know the value of the first term a 1 and the value of the last term a n. There are two ways to find the sum of a finite arithmetic sequence. The sum of an infinite arithmetic sequence is either ∞, if d > 0, or – ∞, if d < 0. ![]() An arithmetic sequence can also be defined recursively by the formulas a 1 = c, a n+1 = a n + d, in which d is again the common difference between consecutive terms, and c is a constant. An arithmetic sequence can be defined by an explicit formula in which a n = d ( n – 1) + c, where d is the common difference between consecutive terms, and c = a 1. What Is the 100th term of the Arithmetic Sequence 1/4, 1/2, 3/4, … Using Arithmetic Sequence Explicit Formula?Īn arithmetic sequence is a sequence in which the difference between each consecutive term is constant.What Are the Applications of Arithmetic Sequence Explicit Formula?.How To Derive Arithmetic Sequence Explicit Formula?.What Is Arithmetic Sequence Explicit Formula?. ![]() ![]()
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