a sequence is defined recursively using the formula $f(n+1) = -0.5f(n)$. if the first term of the sequence is 120, what is $f(5)$?

-15
-7.5
7.5
15

Question

a sequence is defined recursively using the formula $f(n+1) = -0.5f(n)$. if the first term of the sequence is 120, what is $f(5)$?

-15
-7.5
7.5
15

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Geometric Sequences", "Recursive Formulas" ], "current_concepts": [ "Geometric Sequences", "Recursive Formulas" ] } ## Identify the given parameters and recursive relation $$ \begin{aligned} f(1) &= 120 \ f(n+1) &= -0.5 f(n) \end{aligned} $$ ## Compute successive terms of the sequence $$ \begin{aligned} f(2) &= -0.5 \cdot f(1) = -0.5 \cdot 120 = -60 \ f(3) &= -0.5 \cdot f(2) = -0.5 \cdot (-60) = 30 \ f(4) &= -0.5 \cdot f(3) = -0.5 \cdot 30 = -15 \ f(5) &= -0.5 \cdot f(4) = -0.5 \cdot (-15) = 7.5 \end{aligned} $$ ## Match with the given options $$ f(5) = 7.5 $$

-15

-7.5

7.5

15

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

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QUESTION IMAGE

Question

Explanation:

Identify the given parameters and recursive relation

Compute successive terms of the sequence

Match with the given options

Answer: