calculate the $11^{\text{th}}$ term of this arithmetic sequence.

\14, 22, 30, 38, \dots\

Question

calculate the $11^{\text{th}}$ term of this arithmetic sequence.

\14, 22, 30, 38, \dots\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Arithmetic Sequence", "nth Term Rule", "Common Difference" ], "new_concepts": [], "current_concepts": [ "Arithmetic Sequence", "nth Term Rule", "Common Difference" ] } ## Identify the first term and common difference $$ \begin{aligned} a &= 14 \ d &= 22 - 14 = 8 \end{aligned} $$ ## Apply the nth term formula $$ \begin{aligned} a_n &= a + (n - 1)d \ a_{11} &= 14 + (11 - 1) \times 8 \end{aligned} $$ ## Calculate the 11th term $$ \begin{aligned} a_{11} &= 14 + 10 \times 8 \ a_{11} &= 14 + 80 \ a_{11} &= 94 \end{aligned} $$ 94 { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Arithmetic Sequence" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the first term and common difference

Apply the nth term formula

Calculate the 11th term

Answer: