![]() ![]() Create a possible scenario for the table provided below. Then each term is nine times the previous term. For example, suppose the common ratio is 9. Each term is the product of the common ratio and the previous term. A recursive formula allows us to find any term of a geometric sequence by using the previous term. 10 How many additions must be performed? 18ġ5 Example 6 Fill in the table below for day 5 and 6. Using Recursive Formulas for Geometric Sequences. But which to use is based your what you prefer and the problem. For example F10 (Where 10 is the subscript) then this means the 10th term in the sequence F. The small subscript is a way to denote which term in the sequence (Starting from 1). 2, _, _, 26 x y 1 2 ? 3 ? 4 26 Total difference between term 1 and term 4 is 24. This is more general and used mostly for Explicit formulas. Arithmetic or Geometric Common Difference:_ or Common Ratio:_ Arithmetic or Geometric Recursive:_ Explicit:_ Recursive:_ Explicit:_ d = 3 none r = 3 none a1 = 3, an = an-1+3 a1 = 3, an = 3(an-1) an = 3+3(n-1) or an = 3n an = 3(3)n-1 an = 3nġ4 Example 5: The table below represents an arithmetic sequence.įind the missing terms of the sequence, showing your method. The recursive equation for an as a function of an-1 (previous term) a1 = _ 1 2(an-1 ) an = _ġ3 Example 4 Determine whether each situation represents an arithmetic or geometric sequence and then find the recursive and explicit equation for each. 1, 2, 4, 8, 16, 32… Remember!! Recursive Formulas have two parts The starting value of a1. ![]() The recursive equation for an as a function of an-1 (previous term) a1 = 2 a2 = 2(3) a3 = 6(3) a4 = 18(3) an = (an-1)(3) an = r (an-1 ) previous term previous term Common ratio Common ratioġ2 Example 3 1, 2, 4, 8, 16, 32… a1 = _ 2(an-1 ) an = _įind the recursive equation for the following geometric sequence. Recursive Formula Geometric Sequence Recursive Formulas have two parts The starting value of a1. Explicit Formula a1 = 2 a2 = 2(3) a3 = 2(3)(3) a4 = 2(3)(3)(3) an = 2 = 2(3)¹ = 2(3)² = 2(3)³ = 3 r = common ratio 2Ĩ Write the explicit equation for the sequenceĮxample 2a: Write the explicit equation for the sequence x2ġ0 Sequence Notation The notation on the on the second table gives us information about the order of the sequence and the position of the number.ġ1 Developing the Recursive Formula for an Geometric SequenceĢ, 6, 18, 54. +3Įssential Questions: How are geometric sequences written as an explicit formula and a recursive formula? Explicit Definition (review): An explicit formula allows direct computation of any term for a sequence a1, a2, a3,, an, Recursive Definition (review): Recursive formula is a formula that is used to determine the next term of a sequence using one or more of the preceding terms.Ĥ Developing the Explicit Formula for an Geometric SequenceĢ, 6, 18, 54. How to write recursive and explicit formulas?Ģ Warm-Up Write an explicit equation for the following arithmetic sequence. 1 4.2B Geometric Explicit and Recursive Sequences
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