![]() Problem 2: First term of the sequence a1 = 9, common ratio r = 4, find the recursive formula of the geometric sequence. Problem 1: First term of the sequence a1 = 24, common difference d = 10, find the recursive formula of the arithmetic sequence. Recursive and Explicit Formulas – Practice Problems Therefore, explicit formula of the given geometric sequence is an = 3 * 4n – 1. Therefore, explicit formula of the given arithmetic sequence is an = 6n + 5.Įxample 4: Find the explicit formula of the following geometric sequence 3, 12, 36, 108, 432,…įirst term a1 = 3, common ratio r = `12/3` = 4 Use nth term formula to find the explicit formula Therefore, recursive formula of the geometric sequence is of the an = an-1 * 3 where a1 = 12.Įxample 3: Find the explicit formula of the following arithmetic sequence 11, 17, 23, 29, 35, 41, 47,…įirst term a1 = 11, common difference d = 17 – 11 = 6 Therefore, recursive formula of the arithmetic sequence is of the an = an-1 + 14 where a1 = 28.Įxample 2: First term of the sequence a1 = 12, common ratio r = 3, find the recursive formula of the geometric sequence. Recursive and Explicit Formulas – Example ProblemsĮxample 1: First term of the sequence a1 = 28, common difference d = 14, find the recursive formula of the arithmetic sequence.įirst term a1 = 28, common difference d = 14. Explicit formula is used to find the nth term of the sequence using one or more preceding terms of the sequence. Recursive formula is used to find the next term of the sequence using one or more preceding terms of the sequence. ![]() Geometric sequence is a sequence of numbers such that the ratio between two successive members of the sequence is a constant. Arithmetic sequence is a sequence of numbers such that the difference between two successive members of the sequence is a constant.
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