natalia is writing a recursive formula to represent the sequence.

(8, 12, 18, 27, \dots)

what value should she use as the common ratio in the formula?

* $\frac{1}{4}$
* $\frac{2}{3}$
* $\frac{3}{2}$
* $\frac{4}{1}$

Question

natalia is writing a recursive formula to represent the sequence.

(8, 12, 18, 27, \dots)

what value should she use as the common ratio in the formula?

* $\frac{1}{4}$
* $\frac{2}{3}$
* $\frac{3}{2}$
* $\frac{4}{1}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Geometric Sequences" ], "new_concepts": [], "current_concepts": [ "Geometric Sequences", "Recursive Formulas" ] } ## Identify consecutive terms of the sequence $$ a_1 = 8,\quad a_2 = 12,\quad a_3 = 18,\quad a_4 = 27 $$ ## Calculate the ratio between consecutive terms $$ \begin{aligned} r_1 &= \frac{a_2}{a_1} = \frac{12}{8} = \frac{3}{2} \ r_2 &= \frac{a_3}{a_2} = \frac{18}{12} = \frac{3}{2} \ r_3 &= \frac{a_4}{a_3} = \frac{27}{18} = \frac{3}{2} \end{aligned} $$ ## Determine the common ratio $$ r = \frac{3}{2} $$

(A) $\frac{1}{4}$

(B) $\frac{2}{3}$

(C) $\frac{3}{2}$

(D) $\frac{4}{1}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Geometric Sequences" ] }

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QUESTION IMAGE

Question

Explanation:

Identify consecutive terms of the sequence

Calculate the ratio between consecutive terms

Determine the common ratio

Answer: