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Formula for recursive geometric sequence3/20/2024 ![]() ![]() How do you convert an explicit formula to a recursive formula? Answer:īy defining the first term and then setting the nth term as a function of the (n-1)th term multiplied by the common ratio. I know that a Arithmetic sequence can be modeled by this: Y Y differenceX+ X + start. I know that a Geometric sequence can be modeled by this: Y Y start ( ratio) X X. How can you write the explicit formula in different equivalent forms? Answer:īy using algebraic manipulation and exponent properties, such as G(n) = a / r^(1-n) or G(n) = a * r^(n) * r^(-1). Shifted Geometric sequence: U0 U 0 start. Then he explores equivalent forms the explicit formula and finds the corresponding recursive formula. Level up on the above skills and collect up to 480 Mastery points Start quiz. Here, we observe that the ratios 50/25010/502/10 are all 1/5. Explicit & recursive formulas for geometric sequences Google Classroom About Transcript Sal finds an explicit formula of a geometric sequence given the first few terms of the sequences. Recursive formulas for geometric sequences Get 3 of 4 questions to level up Explicit formulas for geometric sequences Get 3 of 4 questions to level up Converting recursive & explicit forms of geometric sequences Get 3 of 4 questions to level up Quiz 2. The exponent represents the number of times the common ratio is multiplied to get to the nth term. Recursive formula is ana(n-1)xx1/5 In a Geometric sequence, the ratio of each term to its preceding term is always constant and is known as common ratio r. Another way to determine this sum a geometric series is. ![]() 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. Proposition 4.15 represents a geometric series as the sum of the first nterms of the corresponding geometric sequence. Using Recursive Formulas for Geometric Sequences A recursive formula allows us to find any term of a geometric sequence by using the previous term. The recursive definition of a geometric series and Proposition 4.15 give two different ways to look at geometric series. What does the exponent in the explicit formula represent? Answer: The proof of Proposition 4.15 is Exercise (7). The explicit formula can be found by identifying the first term and the common ratio, then using the formula G(n) = a * r^(n-1), where a is the first term, r is the common ratio, and n is the term number. Sal finds an explicit formula of a geometric sequence given the first few terms of the sequences. How do you find the explicit formula for a geometric sequence? Answer: ![]() A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. ![]()
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