given an arithmetic sequence with $a_1 = 16$ and $a_4 = 25$, find $a_5$.

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Arithmetic Sequence" ], "new_concepts": [], "current_concepts": [ "Arithmetic Sequence" ] } ## Find the common difference $$ \begin{aligned} a_n &= a_1 + (n - 1)d \ a_4 &= a_1 + 3d \ 25 &= 16 + 3d \ 3d &= 9 \ d &= 3 \end{aligned} $$ ## Calculate the fifth term $$ \begin{aligned} a_5 &= a_4 + d \ a_5 &= 25 + 3 \ a_5 &= 28 \end{aligned} $$ 28 { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Arithmetic Sequence" ] }

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Explanation:

Find the common difference

Calculate the fifth term

Answer: