which recursive formula can be used to generate the sequence shown, where $f(1) = 5$ and $n \ge 1$?

$5, -1, -7, -13, -19, \dots$

$\bigcirc$ $f(n + 1) = f(n) + 6$
$\bigcirc$ $f(n) = f(n + 1) - 6$
$\bigcirc$ $f(n + 1) = f(n) - 6$
$\bigcirc$ $f(n + 1) = -6f(n)$

Question

which recursive formula can be used to generate the sequence shown, where $f(1) = 5$ and $n \ge 1$?

$5, -1, -7, -13, -19, \dots$

$\bigcirc$ $f(n + 1) = f(n) + 6$
$\bigcirc$ $f(n) = f(n + 1) - 6$
$\bigcirc$ $f(n + 1) = f(n) - 6$
$\bigcirc$ $f(n + 1) = -6f(n)$

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 common difference of the sequence $$ \begin{aligned} d &= f(2) - f(1) \ d &= -1 - 5 = -6 \end{aligned} $$ ## Verify the common difference for subsequent terms $$ \begin{aligned} f(3) - f(2) &= -7 - (-1) = -6 \ f(4) - f(3) &= -13 - (-7) = -6 \ f(5) - f(4) &= -19 - (-13) = -6 \end{aligned} $$ ## Write the recursive formula $$ f(n + 1) = f(n) - 6 $$

(A) $f(n + 1) = f(n) + 6$

(B) $f(n) = f(n + 1) - 6$

(C) $f(n + 1) = f(n) - 6$

(D) $f(n + 1) = -6f(n)$

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

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QUESTION IMAGE

Question

Explanation:

Identify the common difference of the sequence

Verify the common difference for subsequent terms

Write the recursive formula

Answer: