a sequence can be defined by the explicit formula $a_n = 5 - 3n$. which recursive formula represents the same sequence of numbers?

$a_n = a_{n-1} - 3; a_1 = 5$
$a_n = 5 - 3a_{n-1}; a_1 = 5$
$a_n = a_{n-1} - 3; a_1 = 2$
$a_n = 5 - 3a_{n-1}; a_1 = 2$

Question

a sequence can be defined by the explicit formula $a_n = 5 - 3n$. which recursive formula represents the same sequence of numbers?

$a_n = a_{n-1} - 3; a_1 = 5$
$a_n = 5 - 3a_{n-1}; a_1 = 5$
$a_n = a_{n-1} - 3; a_1 = 2$
$a_n = 5 - 3a_{n-1}; a_1 = 2$

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 Sequences" ], "new_concepts": [], "current_concepts": [ "Arithmetic Sequences", "Recursive Sequences" ] } ## Find the first term of the sequence $$ a_1 = 5 - 3(1) = 2 $$ ## Determine the common difference $$ \begin{aligned} a_2 &= 5 - 3(2) = -1 \ d &= a_2 - a_1 = -1 - 2 = -3 \end{aligned} $$ ## Formulate the recursive relation $$ \begin{aligned} a_n &= a_{n-1} - 3 \ a_1 &= 2 \end{aligned} $$

(A) $a_n = a_{n-1} - 3; a_1 = 5$

(B) $a_n = 5 - 3a_{n-1}; a_1 = 5$

(C) $a_n = a_{n-1} - 3; a_1 = 2$

(D) $a_n = 5 - 3a_{n-1}; a_1 = 2$

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

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QUESTION IMAGE

Question

Explanation:

Find the first term of the sequence

Determine the common difference

Formulate the recursive relation

Answer: