a sequence is defined recursively using the formula $f(n + 1) = f(n) - 5$. which sequence could be generated using this formula?

$1, -5, 25, -125, ...$
$2, 10, 50, 250, ...$
$3, -2, -7, -12, ...$
$4, 9, 14, 19, ...$

Question

a sequence is defined recursively using the formula $f(n + 1) = f(n) - 5$. which sequence could be generated using this formula?

$1, -5, 25, -125, ...$
$2, 10, 50, 250, ...$
$3, -2, -7, -12, ...$
$4, 9, 14, 19, ...$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Recursive Formulas", "Arithmetic Sequences", "Common Difference" ], "new_concepts": [], "current_concepts": [ "Recursive Formulas", "Arithmetic Sequences", "Common Difference" ] } ## Identify the recursive rule and sequence type $$ f(n + 1) = f(n) - 5 $$ $$ d = -5 $$ ## Test the given options with the common difference $$ \begin{aligned} &\text{Option 1: } 1, -5, 25, -125, \dots \implies -5 - 1 = -6 e -5 \ &\text{Option 2: } 2, 10, 50, 250, \dots \implies 10 - 2 = 8 e -5 \ &\text{Option 3: } 3, -2, -7, -12, \dots \implies -2 - 3 = -5, \ -7 - (-2) = -5, \ -12 - (-7) = -5 \ &\text{Option 4: } 4, 9, 14, 19, \dots \implies 9 - 4 = 5 e -5 \end{aligned} $$ ## Select the matching sequence $$ 3, -2, -7, -12, \dots $$

(A) $1, -5, 25, -125, \dots$

(B) $2, 10, 50, 250, \dots$

(C) $3, -2, -7, -12, \dots$

(D) $4, 9, 14, 19, \dots$

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

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QUESTION IMAGE

Question

Explanation:

Identify the recursive rule and sequence type

Test the given options with the common difference

Select the matching sequence

Answer: