the explicit rule for an arithmetic sequence is $a_n = 8.7 + (-1.4)(n-1)$. what is the value of the $47^{\text{th}}$ term? round to the nearest tenth, if necessary.

$\bigcirc$ $-55.7$
$\bigcirc$ $-26.4$
$\bigcirc$ $45.6$
$\bigcirc$ $65.8$

Question

the explicit rule for an arithmetic sequence is $a_n = 8.7 + (-1.4)(n-1)$. what is the value of the $47^{\text{th}}$ term? round to the nearest tenth, if necessary.

$\bigcirc$ $-55.7$
$\bigcirc$ $-26.4$
$\bigcirc$ $45.6$
$\bigcirc$ $65.8$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Arithmetic Sequence Explicit Formula", "Explicit Sequence Evaluation" ], "new_concepts": [], "current_concepts": [ "Arithmetic Sequence Explicit Formula", "Explicit Sequence Evaluation" ] } ## Identify the given explicit rule Using the *Arithmetic Sequence Explicit Formula* knowledge point $$ a_n = 8.7 + (-1.4)(n - 1) $$ ## Substitute the term index Using the *Explicit Sequence Evaluation* knowledge point $$ \begin{aligned} n &= 47 \ a_{47} &= 8.7 + (-1.4)(47 - 1) \end{aligned} $$ ## Simplify the expression Using the *Explicit Sequence Evaluation* knowledge point $$ \begin{aligned} a_{47} &= 8.7 + (-1.4)(46) \ a_{47} &= 8.7 - 64.4 \ a_{47} &= -55.7 \end{aligned} $$

(A) $-55.7$

(B) $-26.4$

(C) $45.6$

(D) $65.8$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Explicit Sequence Evaluation" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given explicit rule

Substitute the term index

Simplify the expression

Answer: