Question
Question 1 A)Select ALL of the following that are examples of an arithmetic sequence. (1 point) Responses 3, 9, 27, 81, 2433, 9, 27, 81, 2433, 9, 27, 81, 2433, 9, 27, 81, 243 1, 11, 21, 25, 31, 381, 11, 21, 25, 31, 381, 11, 21, 25, 31, 381, 11, 21, 25, 31, 38 20, 14, 8, 2, −4, −1020, 14, 8, 2, −4, −1020, 14, 8, 2, −4, −1020, 14, 8, 2, −4, −10 You start at an elevation of 12,000 feet and climb down 1,000 feet per day. You start at an elevation of 12,000 feet and climb down 1,000 feet per day. You add $2 to a piggy bank and add triple the money you added the previous day for one month. You add $2 to a piggy bank and add triple the money you added the previous day for one month. Question 2 A) Given the Recursive Formula: an=an−1+2an=an−1+2 a1 = 5a1 = 5 a4 = an−1 +2a4 = an−1 +2(4 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. What is the common difference? Response area What is the first term? Response area Which term of the sequence does a4a4 represent? Response area Which term does an−1an−1 represent? Response area 4th523rd Question 3 A) Given the explicit formula: a5= 8 + 7(n − 1)a5= 8 + 7(n − 1)(4 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. What is the common difference? Response area What is the first term? Response area What term is the formula finding? Response area What value should replace n? Response area 7856 Question 4 A) Given the explicit formula, find the 5th term. an = −5 +10(n − 1)an = −5 +10(n − 1)(1 point) Responses 45 45 10 10 -25 -25 35 35
Question 6 A) Which function gives the correct recursive formula for the sequence? 2, 7, 12, 17, 22, 272, 7, 12, 17, 22, 27(1 point) Responses a1 = 2; an = an −1 + 7a1 = 2; an = an −1 + 7a1 = 2; an = an −1 + 7a1 = 2; an = an −1 + 7 a1 = 2; an = an −1 +5a1 = 2; an = an −1 +5a1 = 2; an = an −1 +5a1 = 2; an = an −1 +5 a1 = 7; an = an−1 + 2a1 = 7; an = an−1 + 2a1 = 7; an = an−1 + 2a1 = 7; an = an−1 + 2 a1 = 5; an = an −1 +2a1 = 5; an = an −1 +2a1 = 5; an = an −1 +2a1 = 5; an = an −1 +2 Question 7 A)A car has 121,358 miles on its odometer and accumulates an average of 255 more each week. What is the function rule that represents the total number of M miles the car will have on the odometer after w weeks? (1 point) Responses M(w)=121,358+255wM(w)=121,358+255wcap m times w is equal to 121 comma 358 plus 255 w M(w)=121,358w+255wM(w)=121,358w+255wcap m times w is equal to 121 comma 358 w plus 255 w M(w)=121,358+255M(w)=121,358+255cap m times w is equal to 121 comma 358 plus 255 M(w)=121,358w+255M(w)=121,358w+255cap m times w is equal to 121 comma 358 w plus 255 Question 8 A)(6 points) Compare the linear function and the arithmetic sequence below. Linear Function: x y -1 10 0 14 1 18 2 22 The rate of change of the linear function is The y-intercept of the linear function is Arithmetic Sequence (Explicit formula): an = 10+ 4(n−1)an = 10+ 4(n−1) The rate of change (common difference) of the arithmetic sequence is The first value of the arithmetic sequence is The rate of change of this linear function is the rate of change of this arithmetic sequence. Arithmetic sequences can be represented as a linear function.
Question 10 A)Which of the following is UNLIKE the others with respect to the rate of change (common difference)?(1 point) Responses f(x) = 6x − 2f(x) = 6x − 2f(x) = 6x − 2f(x) = 6x − 2 2, 8, 12, 20, 262, 8, 12, 20, 262, 8, 12, 20, 262, 8, 12, 20, 26 an = −5 + 6(n − 1)an = −5 + 6(n − 1)an = −5 + 6(n − 1)an = −5 + 6(n − 1) f(x) = 6x +1f(x) = 6x +1f(x) = 6x +1f(x) = 6x +1 Question 11 A)The population of bunnies in March is 12. A researcher notices that the population is tripling each month. The population can be represented by the equation P = 12(3)xP = 12(3)x where x is the number of months since March. What will the population of bunnies be after 5 months? (1 point) Responses 420 420 180 180 243 243 2916 2916 Question 12 A)Convert the recursive form a1=5, an=2an−1a1=5, an=2an−1 to the explicit form. (1 point) Responses an=2(5)n−1an=2(5)n−1A sub n is equal to 2 times 5 raised to the n minus 1 power an=3(7)nan=3(7)nA sub n is equal to 3 times 7 to the n th power an=5(2)n+1an=5(2)n+1A sub n is equal to 5 times 2 raised to the n plus 1 power an=5(2)n−1an=5(2)n−1A sub n is equal to 5 times 2 raised to the n minus 1 power Question 13 A)Given: an=12(13)n−1an=12(13)n−1 match the term to its answer. Answers may be used more than once.(3 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. Common Ratio a1a1 a2a2 131341212
Question 6 A) Which function gives the correct recursive formula for the sequence? 2, 7, 12, 17, 22, 272, 7, 12, 17, 22, 27(1 point) Responses a1 = 2; an = an −1 + 7a1 = 2; an = an −1 + 7a1 = 2; an = an −1 + 7a1 = 2; an = an −1 + 7 a1 = 2; an = an −1 +5a1 = 2; an = an −1 +5a1 = 2; an = an −1 +5a1 = 2; an = an −1 +5 a1 = 7; an = an−1 + 2a1 = 7; an = an−1 + 2a1 = 7; an = an−1 + 2a1 = 7; an = an−1 + 2 a1 = 5; an = an −1 +2a1 = 5; an = an −1 +2a1 = 5; an = an −1 +2a1 = 5; an = an −1 +2 Question 7 A)A car has 121,358 miles on its odometer and accumulates an average of 255 more each week. What is the function rule that represents the total number of M miles the car will have on the odometer after w weeks? (1 point) Responses M(w)=121,358+255wM(w)=121,358+255wcap m times w is equal to 121 comma 358 plus 255 w M(w)=121,358w+255wM(w)=121,358w+255wcap m times w is equal to 121 comma 358 w plus 255 w M(w)=121,358+255M(w)=121,358+255cap m times w is equal to 121 comma 358 plus 255 M(w)=121,358w+255M(w)=121,358w+255cap m times w is equal to 121 comma 358 w plus 255 Question 8 A)(6 points) Compare the linear function and the arithmetic sequence below. Linear Function: x y -1 10 0 14 1 18 2 22 The rate of change of the linear function is The y-intercept of the linear function is Arithmetic Sequence (Explicit formula): an = 10+ 4(n−1)an = 10+ 4(n−1) The rate of change (common difference) of the arithmetic sequence is The first value of the arithmetic sequence is The rate of change of this linear function is the rate of change of this arithmetic sequence. Arithmetic sequences can be represented as a linear function.
Question 10 A)Which of the following is UNLIKE the others with respect to the rate of change (common difference)?(1 point) Responses f(x) = 6x − 2f(x) = 6x − 2f(x) = 6x − 2f(x) = 6x − 2 2, 8, 12, 20, 262, 8, 12, 20, 262, 8, 12, 20, 262, 8, 12, 20, 26 an = −5 + 6(n − 1)an = −5 + 6(n − 1)an = −5 + 6(n − 1)an = −5 + 6(n − 1) f(x) = 6x +1f(x) = 6x +1f(x) = 6x +1f(x) = 6x +1 Question 11 A)The population of bunnies in March is 12. A researcher notices that the population is tripling each month. The population can be represented by the equation P = 12(3)xP = 12(3)x where x is the number of months since March. What will the population of bunnies be after 5 months? (1 point) Responses 420 420 180 180 243 243 2916 2916 Question 12 A)Convert the recursive form a1=5, an=2an−1a1=5, an=2an−1 to the explicit form. (1 point) Responses an=2(5)n−1an=2(5)n−1A sub n is equal to 2 times 5 raised to the n minus 1 power an=3(7)nan=3(7)nA sub n is equal to 3 times 7 to the n th power an=5(2)n+1an=5(2)n+1A sub n is equal to 5 times 2 raised to the n plus 1 power an=5(2)n−1an=5(2)n−1A sub n is equal to 5 times 2 raised to the n minus 1 power Question 13 A)Given: an=12(13)n−1an=12(13)n−1 match the term to its answer. Answers may be used more than once.(3 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. Common Ratio a1a1 a2a2 131341212
Answers
GPT-4o mini
**Question 1:**
A) Select ALL of the following that are examples of an arithmetic sequence.
- The arithmetic sequence has a constant difference between consecutive terms.
- 3, 9, 27, 81, 243 ➔ Not an arithmetic sequence (these are powers of 3).
- 1, 11, 21, 25, 31, 38 ➔ Arithmetic sequence (common difference is 10).
- 20, 14, 8, 2, -4, -10 ➔ Arithmetic sequence (common difference is -6).
- You start at an elevation of 12,000 feet and climb down 1,000 feet per day ➔ Arithmetic sequence (common difference is -1000).
- You add $2 to a piggy bank and add triple the money you added the previous day for one month ➔ Not an arithmetic sequence (this is a geometric sequence where the ratio varies).
**Responses:**
- 1, 11, 21, 25, 31, 38
- 20, 14, 8, 2, -4, -10
- You start at an elevation of 12,000 feet and climb down 1,000 feet per day.
---
**Question 2:**
A) Given the Recursive Formula:
an=an−1+2 with a1 = 5
- What is the common difference? **2**
- What is the first term? **5**
- Which term of the sequence does a4 represent? **4th**
- Which term does an−1 represent? **3rd**
---
**Question 3:**
A) Given the explicit formula: a5= 8 + 7(n − 1)
- What is the common difference? **7**
- What is the first term? **8**
- What term is the formula finding? **5**
- What value should replace n? **5**
---
**Question 4:**
A) Given the explicit formula, find the 5th term.
an = −5 + 10(n − 1)
- To find the 5th term (n=5):
a5 = -5 + 10(5 - 1)
a5 = -5 + 10(4)
a5 = -5 + 40
a5 = 35.
**Responses:** 35
---
**Question 6:**
A) Which function gives the correct recursive formula for the sequence: 2, 7, 12, 17, 22, 27
- The common difference is 5.
- The recursive formula is: a1 = 2; an = an − 1 + 5.
**Response:**
a1 = 2; an = an − 1 + 5
---
**Question 7:**
A) A car has 121,358 miles on its odometer and accumulates an average of 255 more each week.
- What is the function rule that represents the total number of M miles the car will have on the odometer after w weeks?
**Response:** M(w)=121,358+255w
---
**Question 8:**
A) Compare the linear function and the arithmetic sequence below.
- Linear Function's rate of change: **4** (from the table, y-values change by 4 with each x increment).
- Y-intercept of the linear function: **14** (when x=0).
- Arithmetic Sequence (Explicit formula): an = 10 + 4(n−1),
- Rate of change (common difference): **4**
- First value of the arithmetic sequence: **10**
---
**Question 10:**
A) Which of the following is UNLIKE the others with respect to the rate of change (common difference)?
- f(x) = 6x − 2 (rate of change is 6).
- 2, 8, 12, 20, 26 (common difference is not constant; differences are 6, 4, 8, 6).
- an = −5 + 6(n − 1) (common difference is 6).
- f(x) = 6x + 1 (rate of change is 6).
**Response:**
2, 8, 12, 20, 26 (is unlike the others).
---
**Question 11:**
A) The population of bunnies in March is 12. The population is tripling each month.
- The equation is: P = 12(3)^x.
- After 5 months: P = 12(3)^5 = 12 * 243 = 2916.
**Responses:** 2916
---
**Question 12:**
A) Convert the recursive form a1=5, an=2an−1 to explicit form.
- The explicit form can be expressed as: an=5(2)^(n−1).
**Responses:** an=5(2)^(n−1)
---
**Question 13:**
A) Given: an=12(13)^(n−1), match the term to its answer.
- Common Ratio: **13**
- a1: **12**
- a2: **156** (12 * 13)
**Responses:**
- Common Ratio: 13
- a1: 12
- a2: 156 (not listed in original options, please adjust accordingly) but answers might vary with formats in the question.
A) Select ALL of the following that are examples of an arithmetic sequence.
- The arithmetic sequence has a constant difference between consecutive terms.
- 3, 9, 27, 81, 243 ➔ Not an arithmetic sequence (these are powers of 3).
- 1, 11, 21, 25, 31, 38 ➔ Arithmetic sequence (common difference is 10).
- 20, 14, 8, 2, -4, -10 ➔ Arithmetic sequence (common difference is -6).
- You start at an elevation of 12,000 feet and climb down 1,000 feet per day ➔ Arithmetic sequence (common difference is -1000).
- You add $2 to a piggy bank and add triple the money you added the previous day for one month ➔ Not an arithmetic sequence (this is a geometric sequence where the ratio varies).
**Responses:**
- 1, 11, 21, 25, 31, 38
- 20, 14, 8, 2, -4, -10
- You start at an elevation of 12,000 feet and climb down 1,000 feet per day.
---
**Question 2:**
A) Given the Recursive Formula:
an=an−1+2 with a1 = 5
- What is the common difference? **2**
- What is the first term? **5**
- Which term of the sequence does a4 represent? **4th**
- Which term does an−1 represent? **3rd**
---
**Question 3:**
A) Given the explicit formula: a5= 8 + 7(n − 1)
- What is the common difference? **7**
- What is the first term? **8**
- What term is the formula finding? **5**
- What value should replace n? **5**
---
**Question 4:**
A) Given the explicit formula, find the 5th term.
an = −5 + 10(n − 1)
- To find the 5th term (n=5):
a5 = -5 + 10(5 - 1)
a5 = -5 + 10(4)
a5 = -5 + 40
a5 = 35.
**Responses:** 35
---
**Question 6:**
A) Which function gives the correct recursive formula for the sequence: 2, 7, 12, 17, 22, 27
- The common difference is 5.
- The recursive formula is: a1 = 2; an = an − 1 + 5.
**Response:**
a1 = 2; an = an − 1 + 5
---
**Question 7:**
A) A car has 121,358 miles on its odometer and accumulates an average of 255 more each week.
- What is the function rule that represents the total number of M miles the car will have on the odometer after w weeks?
**Response:** M(w)=121,358+255w
---
**Question 8:**
A) Compare the linear function and the arithmetic sequence below.
- Linear Function's rate of change: **4** (from the table, y-values change by 4 with each x increment).
- Y-intercept of the linear function: **14** (when x=0).
- Arithmetic Sequence (Explicit formula): an = 10 + 4(n−1),
- Rate of change (common difference): **4**
- First value of the arithmetic sequence: **10**
---
**Question 10:**
A) Which of the following is UNLIKE the others with respect to the rate of change (common difference)?
- f(x) = 6x − 2 (rate of change is 6).
- 2, 8, 12, 20, 26 (common difference is not constant; differences are 6, 4, 8, 6).
- an = −5 + 6(n − 1) (common difference is 6).
- f(x) = 6x + 1 (rate of change is 6).
**Response:**
2, 8, 12, 20, 26 (is unlike the others).
---
**Question 11:**
A) The population of bunnies in March is 12. The population is tripling each month.
- The equation is: P = 12(3)^x.
- After 5 months: P = 12(3)^5 = 12 * 243 = 2916.
**Responses:** 2916
---
**Question 12:**
A) Convert the recursive form a1=5, an=2an−1 to explicit form.
- The explicit form can be expressed as: an=5(2)^(n−1).
**Responses:** an=5(2)^(n−1)
---
**Question 13:**
A) Given: an=12(13)^(n−1), match the term to its answer.
- Common Ratio: **13**
- a1: **12**
- a2: **156** (12 * 13)
**Responses:**
- Common Ratio: 13
- a1: 12
- a2: 156 (not listed in original options, please adjust accordingly) but answers might vary with formats in the question.
number 13 responses are 1/3, 12 and 4
GPT-4o mini
Thank you for your input. Given the responses for Question 13:
- Common Ratio: **1/3**
- a1: **12**
- a2: **4**
The responses can be matched to their respective terms:
1. **Common Ratio:** 1/3 - This indicates that each term in the sequence is produced by multiplying the previous term by 1/3.
2. **a1:** 12 - This is the first term of the sequence.
3. **a2:** 4 - This likely indicates the second term in a different sequence or derived from a context not directly indicated in the previous equations.
So based on your new information, the answers would be:
- **Common Ratio:** 1/3
- **a1:** 12
- **a2:** 4
If you need further assistance or clarification on this or other questions, feel free to ask!
- Common Ratio: **1/3**
- a1: **12**
- a2: **4**
The responses can be matched to their respective terms:
1. **Common Ratio:** 1/3 - This indicates that each term in the sequence is produced by multiplying the previous term by 1/3.
2. **a1:** 12 - This is the first term of the sequence.
3. **a2:** 4 - This likely indicates the second term in a different sequence or derived from a context not directly indicated in the previous equations.
So based on your new information, the answers would be:
- **Common Ratio:** 1/3
- **a1:** 12
- **a2:** 4
If you need further assistance or clarification on this or other questions, feel free to ask!