evaluate each arithmetic series described.
$a_1 = 14, d = 2, n = 20$

- 660
- 662
- 663
- 661

question 8
evaluate each arithmetic series described.
$a_1 = 3, n = 11, a_{11} = -17$

- -71
- -77
- -73
- -75

Question

evaluate each arithmetic series described.
$a_1 = 14, d = 2, n = 20$

- 660
- 662
- 663
- 661

question 8
evaluate each arithmetic series described.
$a_1 = 3, n = 11, a_{11} = -17$

- -71
- -77
- -73
- -75

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "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 Using the *Sum of Arithmetic Series* and *Arithmetic Series* knowledge points $$ \begin{aligned} &a_1 = 14,\quad d = 2,\quad n = 20\ &S_n = \frac{n}{2} [2a_1 + (n - 1)d]\ &S_{20} = \frac{20}{2} [2(14) + (20 - 1)2]\ &S_{20} = 10 [28 + 38] = 10 [66] = 660 \end{aligned} $$ ## Evaluate the second arithmetic series Using the *Sum of Arithmetic Series* and *Arithmetic Series* knowledge points $$ \begin{aligned} &a_1 = 3,\quad n = 11,\quad a_{11} = -17\ &S_n = \frac{n}{2} (a_1 + a_n)\ &S_{11} = \frac{11}{2} (3 + (-17))\ &S_{11} = \frac{11}{2} (-14) = 11(-7) = -77 \end{aligned} $$ ## Question 1 (A) 660

(B) 662

(C) 663

(D) 661 ## Question 2 (A) -71

(B) -77

(C) -73

(D) -75

{ "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