Arithmetic Sequence And Series Quiz!
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Are you experienced with arithmetic sequence and series? An arithmetic sequence is a sequence in which each term is discovered by adding the same value to the previous term. It is a sequence of numbers where the difference between the successive terms is constant. Finding a sequence depends on whether the sequence is arithmetic or geometric. This quiz will tell you if your mathematical knowledge adds up or not.
- 1.
Find the common difference in the Arithmetic Sequence 3,3/14, 7/2, 15/4
- A.
1/4
- B.
3/4
- C.
5/2
- D.
4
Correct Answer
A. 1/4Explanation
The common difference in an arithmetic sequence is the constant value that is added or subtracted to each term to get the next term. In this case, we can see that each term is obtained by adding 1/4 to the previous term. Therefore, the common difference in this arithmetic sequence is 1/4.Rate this question:
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- 2.
What is the sum of all odd integers between 8 and 26?
- A.
153
- B.
151
- C.
149
- D.
148
Correct Answer
A. 153Explanation
The sum of all odd integers between 8 and 26 can be found by adding all the odd numbers in that range. The odd numbers between 8 and 26 are 9, 11, 13, 15, 17, 19, 21, 23, and 25. Adding these numbers together, we get 153.Rate this question:
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- 3.
If three arithmetic means are inserted between 11 and 39, find the 2nd arithmetic mean.
- A.
46.8
- B.
32
- C.
25
- D.
18
Correct Answer
C. 25Explanation
To insert three arithmetic means between 11 and 39, we calculate the sequence's common difference, finding it to be 7. Placing the means creates a sequence where each term increases by 7 from the previous one. The second arithmetic mean, positioned as the third term in this sequence, is calculated as 11 plus twice the common difference (14), resulting in 25, aligning with arithmetic sequence principles.Rate this question:
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- 4.
Which term of the Arithmetic Sequence 4,1,-2,-5,... is 29?
- A.
9th term
- B.
10th term
- C.
11th term
- D.
12th term
- E.
None of the above
Correct Answer
D. 12th termExplanation
The common difference in this arithmetic sequence is -3 (each term is 3 less than the previous one). To find out which term is -29, we can follow these steps:
Find the difference between the first term and -29: -29 - 4 = -33
Divide the difference by the common difference: -33 / -3 = 11
Add 1 to the result (because we started with the first term): 11 + 1 = 12
Therefore, -29 is the 12th term of the sequence.Rate this question:
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- 5.
The 1st term of an arithmetic sequence is 2 while the 18th term is 87. Find the common difference of the sequence.
- A.
7
- B.
6
- C.
5
- D.
3
Correct Answer
C. 5Explanation
The common difference of an arithmetic sequence is the constant value added to each term to get the next term. In this case, we can find the common difference by subtracting the 1st term (2) from the 18th term (87). 87 - 2 = 85. Therefore, the common difference of the sequence is 85 divided by the number of terms between the 1st and 18th term, which is 17. 85 / 17 = 5.Rate this question:
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- 6.
Which of the following is the sum of all the multiples of 3 from 15 to 48?
- A.
315
- B.
360
- C.
378
- D.
396
Correct Answer
C. 378Explanation
To find the sum of all the multiples of 3 from 15 to 48, we can use the formula for the sum of an arithmetic series. The first term is 15, the last term is 48, and the common difference is 3. We can calculate the number of terms using the formula (last term - first term) / common difference + 1. In this case, the number of terms is (48 - 15) / 3 + 1 = 12. Then, we can use the formula for the sum of an arithmetic series, which is (number of terms / 2) * (first term + last term). Plugging in the values, we get (12 / 2) * (15 + 48) = 6 * 63 = 378. Therefore, the correct answer is 378.Rate this question:
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- 7.
What is the nth term of the arithmetic sequence 7,9,11,13,15,17,....?
- A.
3n+4
- B.
2n+5
- C.
4n+3
- D.
N+2
Correct Answer
B. 2n+5Explanation
The given sequence starts with 7 and increases by 2 with each term. To find the nth term, we need to determine the pattern. We can see that the first term is obtained by adding 5 to 2 times the position of the term (n). Therefore, the nth term of the sequence can be represented as 2n+5.Rate this question:
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- 8.
Find p so that the numbers 7p+2,5p+12,2p-1,... form an arithmetic sequence.
- A.
-8
- B.
-5
- C.
-13
- D.
-23
Correct Answer
D. -23Explanation
To form an arithmetic sequence, the difference between consecutive terms must be constant. In this case, the common difference can be found by subtracting the second term from the first term: (5p+12) - (7p+2) = -2p + 10. Similarly, the difference between the third and second term is: (2p-1) - (5p+12) = -3p - 13. Since both differences must be equal, we can set them equal to each other and solve for p: -2p + 10 = -3p - 13. Simplifying this equation, we get p = -23. Therefore, the correct answer is -23.Rate this question:
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- 9.
What is the 20th term of the arithmetic sequence 3, 7, 11, 15,...?
- A.
75
- B.
79
- C.
83
- D.
87
Correct Answer
B. 79Explanation
To find the 20th term, we can use the formula for the nth term of an arithmetic sequence:
a_n = a_1 + (n - 1)d
where:
a_n is the nth term
a_1 is the first term
d is the common difference
In this sequence, a_1 = 3 and d = 4. Substituting these values and n = 20 into the formula:
a_20 = 3 + (20 - 1) * 4 a_20 = 3 + 19 * 4 a_20 = 3 + 76 a_20 = 79Rate this question:
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- 10.
Kelly is saving her money to buy a car. She has Php 50,000 and she plans to save Php 3,750 per week from her job as a call center manager. How much will Kelly have saved after 8 weeks?
- A.
Php 76,000
- B.
Php 80,000
- C.
Php 85,000
- D.
Php 76,750
Correct Answer
B. pHp 80,000Explanation
Kelly plans to save Php 3,750 per week for 8 weeks. So, to find out how much she will have saved after 8 weeks, we need to multiply Php 3,750 by 8. Php 3,750 multiplied by 8 equals Php 30,000. Adding this to her initial savings of Php 50,000, Kelly will have a total of Php 80,000.Rate this question:
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Current Version
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Oct 21, 2024Quiz Edited by
ProProfs Editorial Team -
Sep 02, 2020Quiz Created by
Regina Apostol
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