write a recursive formula for each sequence.

(a) write a recursive formula for $5, -10, 20, -40, \dots$
\a_1 = \square\
\a_n = \square \text{ for } n \ge 2\

(b) write a recursive formula for $12, 17, 22, 27, \dots$
\a_1 = \square\
\a_n = \square \text{ for } n \ge 2\

Question

write a recursive formula for each sequence.

(a) write a recursive formula for $5, -10, 20, -40, \dots$
\a_1 = \square\
\a_n = \square \text{ for } n \ge 2\

(b) write a recursive formula for $12, 17, 22, 27, \dots$
\a_1 = \square\
\a_n = \square \text{ for } n \ge 2\

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Geometric Sequences", "Recursive Formulas" ], "new_concepts": [ "Arithmetic Sequences" ], "current_concepts": [ "Geometric Sequences", "Arithmetic Sequences", "Recursive Formulas" ] } ## Determine the recursive formula for sequence (a) $$ \begin{aligned} &a_1 = 5\ &r = \frac{-10}{5} = -2\ &a_n = -2a_{n-1} \quad \text{for } n \ge 2 \end{aligned} $$ ## Determine the recursive formula for sequence (b) $$ \begin{aligned} &a_1 = 12\ &d = 17 - 12 = 5\ &a_n = a_{n-1} + 5 \quad \text{for } n \ge 2 \end{aligned} $$ ## Question 1 (a) Write a recursive formula for $5, -10, 20, -40, \dots$ $a_1 =$ 5 $a_n =$ $-2a_{n-1}$ for $n \ge 2$ ## Question 2 (b) Write a recursive formula for $12, 17, 22, 27, \dots$ $a_1 =$ 12 $a_n =$ $a_{n-1} + 5$ for $n \ge 2$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Recursive Formulas" ] }

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Explanation:

Determine the recursive formula for sequence (a)

Determine the recursive formula for sequence (b)

Answer:

Question 1

Question 2