the total number of miles jeremy walked on a hike can be represented by using the formula $a_n = a_{n-1} + 3$. if $a_1 = 2$ and $n$ represents the total number of hours walked, what is the total distance jeremy walked at the end of each of the first three hours?

2 miles, 5 miles, 8 miles
2 miles, 6 miles, 18 miles
2 miles, 3 miles, 4 miles
2 miles, 4 miles, 6 miles

Question

the total number of miles jeremy walked on a hike can be represented by using the formula \$a_n = a_{n-1} + 3\$. if \$a_1 = 2\$ and \$n\$ represents the total number of hours walked, what is the total distance jeremy walked at the end of each of the first three hours?

2 miles, 5 miles, 8 miles
2 miles, 6 miles, 18 miles
2 miles, 3 miles, 4 miles
2 miles, 4 miles, 6 miles

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Recursive Formulas", "Arithmetic Sequences" ], "new_concepts": [], "current_concepts": [ "Recursive Formulas", "Arithmetic Sequences" ] } ## Identify the given recursive formula and first term $$ \begin{aligned} a_1 &= 2 \ a_n &= a_{n-1} + 3 \end{aligned} $$ ## Calculate the second and third terms $$ \begin{aligned} a_2 &= a_1 + 3 = 2 + 3 = 5 \ a_3 &= a_2 + 3 = 5 + 3 = 8 \end{aligned} $$ ## Match the calculated terms with the options $$ \begin{aligned} a_1 &= 2\text{ miles} \ a_2 &= 5\text{ miles} \ a_3 &= 8\text{ miles} \end{aligned} $$

(A) 2 miles, 5 miles, 8 miles

(B) 2 miles, 6 miles, 18 miles

(C) 2 miles, 3 miles, 4 miles

(D) 2 miles, 4 miles, 6 miles

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

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QUESTION IMAGE

Question

Explanation:

Identify the given recursive formula and first term

Calculate the second and third terms

Match the calculated terms with the options

Answer: