which sequence is generated by the function $f(n + 1) = f(n) - 2$ for $f(1) = 10$?

$\bigcirc$ $-10, -12, -14, -16, -18, \dots$
$\bigcirc$ $-2, 8, 18, 28, 38, \dots$
$\bigcirc$ $8, 18, 28, 38, 48, \dots$
$\bigcirc$ $10, 8, 6, 4, 2, \dots$

Question

which sequence is generated by the function $f(n + 1) = f(n) - 2$ for $f(1) = 10$?

$\bigcirc$ $-10, -12, -14, -16, -18, \dots$
$\bigcirc$ $-2, 8, 18, 28, 38, \dots$
$\bigcirc$ $8, 18, 28, 38, 48, \dots$
$\bigcirc$ $10, 8, 6, 4, 2, \dots$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Arithmetic Sequences", "Recursive Formulas" ], "new_concepts": [], "current_concepts": [ "Arithmetic Sequences", "Recursive Formulas" ] } ## Identify the first term of the sequence $$ f(1) = 10 $$ ## Calculate subsequent terms using the recursive formula $$ \begin{aligned} f(2) &= f(1) - 2 = 10 - 2 = 8 \ f(3) &= f(2) - 2 = 8 - 2 = 6 \ f(4) &= f(3) - 2 = 6 - 2 = 4 \ f(5) &= f(4) - 2 = 4 - 2 = 2 \end{aligned} $$ ## Match the calculated terms to the options $$ 10, 8, 6, 4, 2, \dots $$

(A) $-10, -12, -14, -16, -18, \dots$

(B) $-2, 8, 18, 28, 38, \dots$

(C) $8, 18, 28, 38, 48, \dots$

(D) $10, 8, 6, 4, 2, \dots$

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

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QUESTION IMAGE

Question

Explanation:

Identify the first term of the sequence

Calculate subsequent terms using the recursive formula

Match the calculated terms to the options

Answer: