(-2\frac{2}{3}, -5\frac{1}{3}, -10\frac{2}{3}, -21\frac{1}{3}, -42\frac{2}{3}, ...)

which formula can be used to describe the sequence?

* (f(x + 1) = -2f(x))
* (f(x + 1) = -\frac{1}{2}f(x))
* (f(x + 1) = \frac{1}{2}f(x))
* (f(x + 1) = 2f(x))

Question

(-2\frac{2}{3}, -5\frac{1}{3}, -10\frac{2}{3}, -21\frac{1}{3}, -42\frac{2}{3}, ...)

which formula can be used to describe the sequence?

* (f(x + 1) = -2f(x))
* (f(x + 1) = -\frac{1}{2}f(x))
* (f(x + 1) = \frac{1}{2}f(x))
* (f(x + 1) = 2f(x))

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", "Recursive Formulas" ], "new_concepts": [], "current_concepts": [ "Geometric Sequences", "Recursive Formulas" ] } ## Convert mixed numbers to improper fractions $$ \begin{aligned} f(1) &= -2\frac{2}{3} = -\frac{8}{3}\ f(2) &= -5\frac{1}{3} = -\frac{16}{3}\ f(3) &= -10\frac{2}{3} = -\frac{32}{3}\ f(4) &= -21\frac{1}{3} = -\frac{64}{3} \end{aligned} $$ ## Determine the common ratio $$ \begin{aligned} r &= \frac{f(2)}{f(1)} = \frac{-\frac{16}{3}}{-\frac{8}{3}} = 2\ r &= \frac{f(3)}{f(2)} = \frac{-\frac{32}{3}}{-\frac{16}{3}} = 2 \end{aligned} $$ ## Write the recursive formula $$ f(x+1) = 2f(x) $$

(A) $f(x + 1) = -2f(x)$

(B) $f(x + 1) = -\frac{1}{2}f(x)$

(C) $f(x + 1) = \frac{1}{2}f(x)$

(D) $f(x + 1) = 2f(x)$

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

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QUESTION IMAGE

Question

Explanation:

Convert mixed numbers to improper fractions

Determine the common ratio

Write the recursive formula

Answer: