if $a_2 = 8$, what are the first three terms of the sequence defined by the recursive formula below?

\a_n = 3a_{n-1} + 2\

* 8, 26, 80
* 2, 8, 26
* 8, 2, 0
* 5, 8, 26

Question

if $a_2 = 8$, what are the first three terms of the sequence defined by the recursive formula below?

\a_n = 3a_{n-1} + 2\

* 8, 26, 80
* 2, 8, 26
* 8, 2, 0
* 5, 8, 26

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Recursive Sequences" ], "new_concepts": [], "current_concepts": [ "Recursive Sequences" ] } ## Solve for the first term $$ \begin{aligned} a_2 &= 3a_1 + 2 \ 8 &= 3a_1 + 2 \ 6 &= 3a_1 \ a_1 &= 2 \end{aligned} $$ ## Solve for the third term $$ \begin{aligned} a_3 &= 3a_2 + 2 \ a_3 &= 3(8) + 2 \ a_3 &= 24 + 2 \ a_3 &= 26 \end{aligned} $$ ## List the first three terms $$ \begin{aligned} a_1, a_2, a_3 = 2, 8, 26 \end{aligned} $$

8, 26, 80

2, 8, 26

8, 2, 0

5, 8, 26

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

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QUESTION IMAGE

Question

Explanation:

Solve for the first term

Solve for the third term

List the first three terms

Answer: