19. in an arithmetic sequence, the 10th term ($a_{10}$) is 30, and the common difference is 2. what is the 1st term ($a_1$)?
a. 6
b. 11
c. 12
d. 15

20. a pedometer records the number of steps a person takes as he or she walks. when a pedometer records 3,898 steps taken by a person who covers a distance of 2.25 feet per step, how much distance, to the nearest 0.1 miles, did the person cover?
(note: 1 mile = 5,280 feet)
f. 0.3
g. 0.6
h. 1.7
j. 3.0

Question

19. in an arithmetic sequence, the 10th term ($a_{10}$) is 30, and the common difference is 2. what is the 1st term ($a_1$)?
a. 6
b. 11
c. 12
d. 15

20. a pedometer records the number of steps a person takes as he or she walks. when a pedometer records 3,898 steps taken by a person who covers a distance of 2.25 feet per step, how much distance, to the nearest 0.1 miles, did the person cover?
(note: 1 mile = 5,280 feet)
f. 0.3
g. 0.6
h. 1.7
j. 3.0

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Arithmetic Sequences", "Unit Conversions" ], "new_concepts": [], "current_concepts": [ "Arithmetic Sequences", "Unit Conversions" ] } ## Solve for the first term of the arithmetic sequence $$ \begin{aligned} a_{10} &= a_1 + (10 - 1)d \ 30 &= a_1 + 9(2) \ 30 &= a_1 + 18 \ a_1 &= 12 \end{aligned} $$ ## Calculate total distance in feet and convert to miles $$ \begin{aligned} \text{Total Feet} &= 3,898 \times 2.25 = 8,770.5 \ \text{Total Miles} &= \frac{8,770.5}{5,280} \approx 1.661 \ \text{Rounded Miles} &\approx 1.7 \end{aligned} $$ ## Question 19 A. 6

B. 11

C. 12

D. 15 ## Question 20 F. 0.3

G. 0.6

H. 1.7

J. 3.0

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Arithmetic Sequences" ] }

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QUESTION IMAGE

Question

Explanation:

Solve for the first term of the arithmetic sequence

Calculate total distance in feet and convert to miles

Answer:

Question 19

Question 20