the amount of interest earned on an account can be represented using the recursive formula $a_n = 1.02(a_{n-1})$. if $a_1 = 255.00$, and $n$ represents the number of months the money is invested, what is the balance at the end of each month for the first three months?

$\bigcirc$ \$255.00, \$260.10, \$265.30
$\bigcirc$ \$255.00, \$260.10, \$265.20
$\bigcirc$ \$255.00, \$256.02, \$257.04
$\bigcirc$ \$255.00, \$250.00, \$245.10

Question

the amount of interest earned on an account can be represented using the recursive formula $a_n = 1.02(a_{n-1})$. if $a_1 = 255.00$, and $n$ represents the number of months the money is invested, what is the balance at the end of each month for the first three months?

$\bigcirc$ \$255.00, \$260.10, \$265.30
$\bigcirc$ \$255.00, \$260.10, \$265.20
$\bigcirc$ \$255.00, \$256.02, \$257.04
$\bigcirc$ \$255.00, \$250.00, \$245.10

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", "Geometric Sequences" ] } ## Identify the given recursive sequence parameters $$ \begin{aligned} a_1 &= 255.00 \ a_n &= 1.02(a_{n-1}) \end{aligned} $$ ## Calculate the second term $$ \begin{aligned} a_2 &= 1.02 \times a_1 \ a_2 &= 1.02 \times 255.00 = 260.10 \end{aligned} $$ ## Calculate the third term $$ \begin{aligned} a_3 &= 1.02 \times a_2 \ a_3 &= 1.02 \times 260.10 = 265.302 \approx 265.30 \end{aligned} $$

(A) $255.00, $260.10, $265.30

(B) $255.00, $260.10, $265.20

(C) $255.00, $256.02, $257.04

(D) $255.00, $250.00, $245.10

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

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QUESTION IMAGE

Question

Explanation:

Identify the given recursive sequence parameters

Calculate the second term

Calculate the third term

Answer: