a sequence is defined by the formula $f(n+1)=f(n)-3$. if $f(4)=22$, what is $f(1)$?

10
13
31
34

Question

a sequence is defined by the formula $f(n+1)=f(n)-3$. if $f(4)=22$, what is $f(1)$?

10
13
31
34

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 sequence type and parameters $$ \begin{aligned} &f(n+1) = f(n) - 3 \ &d = -3 \ &f(4) = 22 \end{aligned} $$ ## Express the term formula and solve for the first term $$ \begin{aligned} &f(n) = f(1) + (n-1)d \ &f(4) = f(1) + (4-1)(-3) \ &22 = f(1) - 9 \ &f(1) = 31 \end{aligned} $$

(A) 10

(B) 13

(C) 31

(D) 34

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

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QUESTION IMAGE

Question

Explanation:

Identify the sequence type and parameters

Express the term formula and solve for the first term

Answer: