a sequence is defined recursively using the equation $f(n + 1) = f(n) - 8$. if $f(1) = 100$, what is $f(6)$?

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Question

a sequence is defined recursively using the equation $f(n + 1) = f(n) - 8$. if $f(1) = 100$, what is $f(6)$?

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Arithmetic Sequences", "Recursive Formulas" ], "new_concepts": [], "current_concepts": [ "Arithmetic Sequences", "Recursive Formulas" ] } ## Identify the sequence type and parameters $$ \begin{aligned} &f(n+1) = f(n) - 8 \ &d = -8 \ &f(1) = 100 \end{aligned} $$ ## Formulate the explicit equation $$ \begin{aligned} &f(n) = f(1) + (n - 1)d \ &f(n) = 100 - 8(n - 1) \end{aligned} $$ ## Calculate the value of f(6) $$ \begin{aligned} &f(6) = 100 - 8(6 - 1) \ &f(6) = 100 - 8(5) \ &f(6) = 100 - 40 = 60 \end{aligned} $$

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

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Question

Explanation:

Identify the sequence type and parameters

Formulate the explicit equation

Calculate the value of f(6)

Answer: