martina opens a savings account with an initial deposit and makes no other deposits or withdrawals. she earns interest on her initial deposit. the total amount of money in her savings account at the end of each year is represented by the sequence shown.

100, 105, 110.25, ...

which recursive formula can be used to determine the total amount of money earned in any year based on the amount earned in the previous year?

$f(n + 1) = f(n) + 5$
$f(n + 1) = 5f(n)$
$f(n + 1) = 1.05f(n)$
$f(n + 1) = 0.05f(n)$

Question

martina opens a savings account with an initial deposit and makes no other deposits or withdrawals. she earns interest on her initial deposit. the total amount of money in her savings account at the end of each year is represented by the sequence shown.

100, 105, 110.25, ...

which recursive formula can be used to determine the total amount of money earned in any year based on the amount earned in the previous year?

$f(n + 1) = f(n) + 5$
$f(n + 1) = 5f(n)$
$f(n + 1) = 1.05f(n)$
$f(n + 1) = 0.05f(n)$

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 Formulas" ], "new_concepts": [], "current_concepts": [ "Geometric Sequences", "Recursive Formulas" ] } ## Find the common ratio of the sequence $$ \begin{aligned} r &= \frac{105}{100} = 1.05 \ r &= \frac{110.25}{105} = 1.05 \end{aligned} $$ ## Formulate the recursive relation $$ f(n+1) = 1.05 f(n) $$

(A) $f(n + 1) = f(n) + 5$

(B) $f(n + 1) = 5f(n)$

(C) $f(n + 1) = 1.05f(n)$

(D) $f(n + 1) = 0.05f(n)$

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

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QUESTION IMAGE

Question

Explanation:

Find the common ratio of the sequence

Formulate the recursive relation

Answer: