evaluate each arithmetic series described.
$a_1 = 22$, $d = 6$, $n = 20$

1580
2289
2288
1144

question 4
1 pts
evaluate each arithmetic series described. $a_1 = 3$, $n = 25$, $a_{25} = 99$

1275
1271
1267
1263

Question

evaluate each arithmetic series described.
$a_1 = 22$, $d = 6$, $n = 20$

1580
2289
2288
1144

question 4
1 pts
evaluate each arithmetic series described. $a_1 = 3$, $n = 25$, $a_{25} = 99$

1275
1271
1267
1263

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 $$ \begin{aligned} &a_1 = 22,\quad d = 6,\quad n = 20\ &S_n = \frac{n}{2} [2a_1 + (n - 1)d]\ &S_{20} = \frac{20}{2} [2(22) + (20 - 1)6]\ &S_{20} = 10 [44 + 19 \times 6]\ &S_{20} = 10 [44 + 114] = 10 \times 158 = 1580 \end{aligned} $$ ## Evaluate the second arithmetic series $$ \begin{aligned} &a_1 = 3,\quad n = 25,\quad a_{25} = 99\ &S_n = \frac{n}{2} (a_1 + a_n)\ &S_{25} = \frac{25}{2} (3 + 99)\ &S_{25} = \frac{25}{2} (102)\ &S_{25} = 25 \times 51 = 1275 \end{aligned} $$ ## Question 1 (A) 1580

(B) 2289

(C) 2288

(D) 1144 ## Question 2 (A) 1275

(B) 1271

(C) 1267

(D) 1263

{ "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