which formula can be used to describe the sequence below?

-8, -5, -2, 1, 4, ...

$a_n = -8a_{n-1} + 3; a_1 = -8$
$a_n = 3a_{n-1} - 11; a_1 = -8$
$a_n = 3a_{n-1}; a_1 = -8$
$a_n = a_{n-1} + 3; a_1 = -8$

Question

which formula can be used to describe the sequence below?

-8, -5, -2, 1, 4, ...

$a_n = -8a_{n-1} + 3; a_1 = -8$
$a_n = 3a_{n-1} - 11; a_1 = -8$
$a_n = 3a_{n-1}; a_1 = -8$
$a_n = a_{n-1} + 3; a_1 = -8$

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 first term and common difference $$ \begin{aligned} a_1 &= -8 \ d &= -5 - (-8) = 3 \ d &= -2 - (-5) = 3 \end{aligned} $$ ## Write the recursive formula $$ \begin{aligned} a_n &= a_{n-1} + d \ a_n &= a_{n-1} + 3, \quad a_1 = -8 \end{aligned} $$

(A) $a_n = -8a_{n-1} + 3; a_1 = -8$

(B) $a_n = 3a_{n-1} - 11; a_1 = -8$

(C) $a_n = 3a_{n-1}; a_1 = -8$

(D) $a_n = a_{n-1} + 3; a_1 = -8$

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

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QUESTION IMAGE

Question

Explanation:

Identify the first term and common difference

Write the recursive formula

Answer: