the fifth term of a geometric sequence is 781.25. each term of the sequence is $\frac{1}{5}$ of the value of the following term.

which recursive formula represents the situation?

$a_n = 5a_{n-1}; a_1 = 1.25$

$a_n = \frac{1}{5}a_{n-1}; a_1 = 488,281.25$

$a_n = 5a_{n-1}; a_1 = 488,281.25$

$a_n = \frac{1}{5}a_{n-1}; a_1 = 1.25$

Question

the fifth term of a geometric sequence is 781.25. each term of the sequence is $\frac{1}{5}$ of the value of the following term.

which recursive formula represents the situation?

$a_n = 5a_{n-1}; a_1 = 1.25$

$a_n = \frac{1}{5}a_{n-1}; a_1 = 488,281.25$

$a_n = 5a_{n-1}; a_1 = 488,281.25$

$a_n = \frac{1}{5}a_{n-1}; a_1 = 1.25$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Geometric Sequences", "Recursive Sequences" ], "new_concepts": [], "current_concepts": [ "Geometric Sequences", "Recursive Sequences" ] } ## Determine the common ratio $$ \begin{aligned} &a_n = \frac{1}{5} a_{n+1} \ &a_{n+1} = 5 a_n \ &r = 5 \ &a_n = 5 a_{n-1} \end{aligned} $$ ## Find the first term $$ \begin{aligned} &a_5 = a_1 \cdot r^4 = 781.25 \ &a_1 \cdot 5^4 = 781.25 \ &625 a_1 = 781.25 \ &a_1 = \frac{781.25}{625} = 1.25 \end{aligned} $$ ## Identify the correct recursive formula $$ a_n = 5 a_{n-1}; a_1 = 1.25 $$

(A) $a_n = 5a_{n-1}; a_1 = 1.25$

(B) $a_n = \frac{1}{5}a_{n-1}; a_1 = 488,281.25$

(C) $a_n = 5a_{n-1}; a_1 = 488,281.25$

(D) $a_n = \frac{1}{5}a_{n-1}; a_1 = 1.25$

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

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QUESTION IMAGE

Question

Explanation:

Determine the common ratio

Find the first term

Identify the correct recursive formula

Answer: