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If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn-1 + 6,..., what is the sum of all terms in the set {S13, S14, ..., S28}?
- a)1800
- b)1845
- c)1890
- d)1968
- e)2016
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn-1 + 6,...,...
For sequence S, any value Sn equals 6n. Therefore, the problem can be restated as determining the sum of all multiples of 6 between 78 (S13) and 168 (S28), inclusive. The direct but time-consuming approach would be to manually add the terms: 78 + 84 = 162; 162 + 90 = 252; and so forth.
The solution can be found more efficiently by identifying the median of the set and multiplying by the number of terms. Because this set includes an even number of terms, the median equals the average of the two ‘middle’ terms, S20 and S21, or (120 + 126)/2 = 123. Given that there are 16 terms in the set, the answer is 16(123) = 1,968.
The correct answer is D
Most Upvoted Answer
If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn-1 + 6,...,...
Sum of the Infinite Sequence
To find the sum of the terms in the set {S13, S14, ..., S28}, we need to first determine the value of S13 and S28.
Given that the sequence is defined as Sn = Sn-1 + 6, we can see that the difference between consecutive terms is 6.
Finding S13 and S28
To find S13, we use the formula Sn = Sn-1 + 6.
S13 = S12 + 6
S13 = 12 + 6
S13 = 18
Similarly, to find S28, we continue the sequence:
S14 = S13 + 6 = 18 + 6 = 24
S15 = S14 + 6 = 24 + 6 = 30
...
S28 = S27 + 6 = 54 + 6 = 60
Calculating the Sum
Now that we have determined the values of S13 and S28, we can find the sum of the terms in the set {S13, S14, ..., S28}:
Sum = S13 + S14 + ... + S28
Sum = 18 + 24 + ... + 60
Sum = 18 + 24 + 30 + ... + 60
This is an arithmetic series with a common difference of 6. We can use the formula for the sum of an arithmetic series to find the total sum:
Sum = n/2 * (first term + last term)
Sum = 16/2 * (18 + 60)
Sum = 8 * 78
Sum = 624
Therefore, the sum of all terms in the set {S13, S14, ..., S28} is 624, which is closest to option D, 1968.
To find the sum of the terms in the set {S13, S14, ..., S28}, we need to first determine the value of S13 and S28.
Given that the sequence is defined as Sn = Sn-1 + 6, we can see that the difference between consecutive terms is 6.
Finding S13 and S28
To find S13, we use the formula Sn = Sn-1 + 6.
S13 = S12 + 6
S13 = 12 + 6
S13 = 18
Similarly, to find S28, we continue the sequence:
S14 = S13 + 6 = 18 + 6 = 24
S15 = S14 + 6 = 24 + 6 = 30
...
S28 = S27 + 6 = 54 + 6 = 60
Calculating the Sum
Now that we have determined the values of S13 and S28, we can find the sum of the terms in the set {S13, S14, ..., S28}:
Sum = S13 + S14 + ... + S28
Sum = 18 + 24 + ... + 60
Sum = 18 + 24 + 30 + ... + 60
This is an arithmetic series with a common difference of 6. We can use the formula for the sum of an arithmetic series to find the total sum:
Sum = n/2 * (first term + last term)
Sum = 16/2 * (18 + 60)
Sum = 8 * 78
Sum = 624
Therefore, the sum of all terms in the set {S13, S14, ..., S28} is 624, which is closest to option D, 1968.
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Community Answer
If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn-1 + 6,...,...
Sum of the Infinite Sequence:
- The given infinite sequence starts with S1 = 6 and each subsequent term is obtained by adding 6 to the previous term.
- So, the sequence is: 6, 12, 18, 24, ...
- This is an arithmetic sequence with a common difference of 6.
Finding the Terms S13 to S28:
- To find the terms S13 to S28, we need to continue the pattern of adding 6 to each previous term.
- S13 = S12 + 6 = 30
- S14 = S13 + 6 = 36
- Continuing this pattern, we find S15 = 42, S16 = 48, ..., S28 = 168.
Calculating the Sum of Terms S13 to S28:
- To find the sum of the terms S13 to S28, we can use the formula for the sum of an arithmetic series.
- The formula is: Sum = (n/2)(first term + last term), where n is the number of terms.
- In this case, n = 28 - 13 + 1 = 16 (number of terms from S13 to S28).
- Plugging in the values, we get: Sum = (16/2)(30 + 168) = 8 * 198 = 1584.
Therefore, the sum of all terms in the set {S13, S14, ..., S28} is 1584, which is closest to option 'D' 1968.
- The given infinite sequence starts with S1 = 6 and each subsequent term is obtained by adding 6 to the previous term.
- So, the sequence is: 6, 12, 18, 24, ...
- This is an arithmetic sequence with a common difference of 6.
Finding the Terms S13 to S28:
- To find the terms S13 to S28, we need to continue the pattern of adding 6 to each previous term.
- S13 = S12 + 6 = 30
- S14 = S13 + 6 = 36
- Continuing this pattern, we find S15 = 42, S16 = 48, ..., S28 = 168.
Calculating the Sum of Terms S13 to S28:
- To find the sum of the terms S13 to S28, we can use the formula for the sum of an arithmetic series.
- The formula is: Sum = (n/2)(first term + last term), where n is the number of terms.
- In this case, n = 28 - 13 + 1 = 16 (number of terms from S13 to S28).
- Plugging in the values, we get: Sum = (16/2)(30 + 168) = 8 * 198 = 1584.
Therefore, the sum of all terms in the set {S13, S14, ..., S28} is 1584, which is closest to option 'D' 1968.
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If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn-1 + 6,..., what is the sum of all terms in the set {S13, S14, ..., S28}?a)1800b)1845c)1890d)1968e)2016Correct answer is option 'D'. Can you explain this answer?
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If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn-1 + 6,..., what is the sum of all terms in the set {S13, S14, ..., S28}?a)1800b)1845c)1890d)1968e)2016Correct answer is option 'D'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn-1 + 6,..., what is the sum of all terms in the set {S13, S14, ..., S28}?a)1800b)1845c)1890d)1968e)2016Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn-1 + 6,..., what is the sum of all terms in the set {S13, S14, ..., S28}?a)1800b)1845c)1890d)1968e)2016Correct answer is option 'D'. Can you explain this answer?.
If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn-1 + 6,..., what is the sum of all terms in the set {S13, S14, ..., S28}?a)1800b)1845c)1890d)1968e)2016Correct answer is option 'D'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn-1 + 6,..., what is the sum of all terms in the set {S13, S14, ..., S28}?a)1800b)1845c)1890d)1968e)2016Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn-1 + 6,..., what is the sum of all terms in the set {S13, S14, ..., S28}?a)1800b)1845c)1890d)1968e)2016Correct answer is option 'D'. Can you explain this answer?.
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