use the formula (s_n = \frac{n(a_1 + a_n)}{2}) to evaluate the following sum.

\sum_{k=1}^{12} (-4 + (k - 1) \cdot 3)

(s_{12} =)

Question

use the formula (s_n = \frac{n(a_1 + a_n)}{2}) to evaluate the following sum.

\sum_{k=1}^{12} (-4 + (k - 1) \cdot 3)

(s_{12} =)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Arithmetic Series", "Sigma Notation", "Summation Formula" ], "new_concepts": [], "current_concepts": [ "Arithmetic Series", "Sigma Notation", "Summation Formula" ] } ## Identify the parameters of the arithmetic series $$ \begin{aligned} &n = 12 \ &a_1 = -4 + (1 - 1) \cdot 3 = -4 \ &a_{12} = -4 + (12 - 1) \cdot 3 = -4 + 33 = 29 \end{aligned} $$ ## Apply the arithmetic series sum formula $$ \begin{aligned} &S_{12} = \frac{12 \cdot (a_1 + a_{12})}{2} \ &S_{12} = 6 \cdot (-4 + 29) \ &S_{12} = 6 \cdot 25 = 150 \end{aligned} $$ Use the formula $S_n = \frac{n(a_1 + a_n)}{2}$ to evaluate the following sum. $$\sum_{k=1}^{12} (-4 + (k - 1) \cdot 3)$$ $S_{12} =$ 150 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Arithmetic Series" ] }

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Question

Explanation:

Identify the parameters of the arithmetic series

Apply the arithmetic series sum formula

Answer: