\\sum_{i=2}^{4} (2a_i + 8i) =\

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Summation Notation", "Sigma Notation Evaluation" ], "current_concepts": [ "Summation Notation", "Sigma Notation Evaluation" ] } ## Expandir los términos de la sumatoria $$ \sum_{i=2}^{4} (2ai + 8i) = (2a(2) + 8(2)) + (2a(3) + 8(3)) + (2a(4) + 8(4)) $$ ## Simplificar cada término individual $$ \begin{aligned} i=2: \quad & 4a + 16 \ i=3: \quad & 6a + 24 \ i=4: \quad & 8a + 32 \end{aligned} $$ ## Sumar los términos semejantes $$ \begin{aligned} \sum_{i=2}^{4} (2ai + 8i) &= (4a + 6a + 8a) + (16 + 24 + 32) \ &= 18a + 72 \end{aligned} $$ $$\sum_{i=2}^{4} (2ai + 8i) =$$ $18a + 72$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Summation Notation" ] }

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Explanation:

Expandir los términos de la sumatoria

Simplificar cada término individual

Sumar los términos semejantes

Answer: