evaluate each arithmetic series described.
$a_1 = 3, n = 7, a_7 = 33$

- 126
- 131
- 121
- 116

question 6
evaluate each arithmetic series described.
$a_1 = -18, d = -9, n = 14$

- -1071
- -1063
- -2142
- -2126

Question

evaluate each arithmetic series described.
$a_1 = 3, n = 7, a_7 = 33$

- 126
- 131
- 121
- 116

question 6
evaluate each arithmetic series described.
$a_1 = -18, d = -9, n = 14$

- -1071
- -1063
- -2142
- -2126

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Arithmetic Series", "Sum of Arithmetic Series" ], "new_concepts": [], "current_concepts": [ "Arithmetic Series", "Sum of Arithmetic Series" ] } ## Evaluate the first arithmetic series $$ \begin{aligned} &a_1 = 3,\quad n = 7,\quad a_7 = 33\ &S_n = \frac{n(a_1 + a_n)}{2}\ &S_7 = \frac{7(3 + 33)}{2} = \frac{7 \times 36}{2} = 7 \times 18 = 126 \end{aligned} $$ ## Evaluate the second arithmetic series $$ \begin{aligned} &a_1 = -18,\quad d = -9,\quad n = 14\ &S_n = \frac{n}{2}[2a_1 + (n-1)d]\ &S_{14} = \frac{14}{2}[2(-18) + (14-1)(-9)]\ &S_{14} = 7[-36 + 13(-9)] = 7[-36 - 117] = 7[-153] = -1071 \end{aligned} $$ ## Question 1 (A) 126

(B) 131

(C) 121

(D) 116 ## Question 2 (A) -1071

(B) -1063

(C) -2142

(D) -2126

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Sum of Arithmetic Series" ] }

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QUESTION IMAGE

Question

Explanation:

Evaluate the first arithmetic series

Evaluate the second arithmetic series

Answer:

Question 1

Question 2