write a recursive formula for each sequence.

(a) write a recursive formula for $49, 38, 27, 16, \dots$

$a_1 = \square$
$a_n = \square$ for $n \ge 2$

(b) write a recursive formula for $300, 30, 3, \frac{3}{10}, \dots$

$a_1 = \square$
$a_n = \square$ for $n \ge 2$

Question

write a recursive formula for each sequence.

(a) write a recursive formula for $49, 38, 27, 16, \dots$

$a_1 = \square$
$a_n = \square$ for $n \ge 2$

(b) write a recursive formula for $300, 30, 3, \frac{3}{10}, \dots$

$a_1 = \square$
$a_n = \square$ 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": [ "Arithmetic Sequences", "Geometric Sequences", "Recursive Formulas" ], "new_concepts": [], "current_concepts": [ "Arithmetic Sequences", "Geometric Sequences", "Recursive Formulas" ] } ## Analyze sequence (a) $$ \begin{aligned} &a_1 = 49 \ &d = 38 - 49 = -11 \ &a_n = a_{n-1} - 11 \end{aligned} $$ ## Analyze sequence (b) $$ \begin{aligned} &a_1 = 300 \ &r = \frac{30}{300} = \frac{1}{10} \ &a_n = \frac{1}{10}a_{n-1} \end{aligned} $$ ## Question 1 (a) Write a recursive formula for $49, 38, 27, 16, \dots$ $a_1 =$ 49 $a_n =$ $a_{n-1} - 11$ for $n \ge 2$ ## Question 2 (b) Write a recursive formula for $300, 30, 3, \frac{3}{10}, \dots$ $a_1 =$ 300 $a_n =$ $\frac{1}{10}a_{n-1}$ for $n \ge 2$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Recursive Formulas" ] }

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Explanation:

Analyze sequence (a)

Analyze sequence (b)

Answer:

Question 1

Question 2