which formula can be used to describe the sequence below?

(27, 9, 3, 1, \frac{1}{3}, \dots)

* (a_n = -3a_{n-1}; a_1 = 27)
* (a_n = \frac{1}{3}a_{n-1}; a_1 = 27)
* (a_n = a_{n-1} - 3; a_1 = 27)
* (a_n = 3a_{n-1} - \frac{1}{3}; a_1 = 27)

Question

which formula can be used to describe the sequence below?

(27, 9, 3, 1, \frac{1}{3}, \dots)

* (a_n = -3a_{n-1}; a_1 = 27)
* (a_n = \frac{1}{3}a_{n-1}; a_1 = 27)
* (a_n = a_{n-1} - 3; a_1 = 27)
* (a_n = 3a_{n-1} - \frac{1}{3}; a_1 = 27)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Recursive Formulas" ], "new_concepts": [ "Geometric Sequences" ], "current_concepts": [ "Recursive Formulas", "Geometric Sequences" ] } ## Identify the first term and common ratio $$ \begin{aligned} a_1 &= 27 \ r &= \frac{9}{27} = \frac{3}{9} = \frac{1}{3} \end{aligned} $$ ## Write the recursive formula $$ \begin{aligned} a_n &= r \cdot a_{n-1} \ a_n &= \frac{1}{3} a_{n-1}, \quad a_1 = 27 \end{aligned} $$

(A) $a_n = -3a_{n-1}; a_1 = 27$

(B) $a_n = \frac{1}{3}a_{n-1}; a_1 = 27$

(C) $a_n = a_{n-1} - 3; a_1 = 27$

(D) $a_n = 3a_{n-1} - \frac{1}{3}; a_1 = 27$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Recursive Formulas" ] }

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Question

Explanation:

Identify the first term and common ratio

Write the recursive formula

Answer: