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Updated on: 10 Apr 2026, 06:15
Originally posted by EgmatQuantExpert on 12 Oct 2018, 04:10.
Last edited by Bunuel on 10 Apr 2026, 06:15, edited 2 times in total.
Last edited by Bunuel on 10 Apr 2026, 06:15, edited 2 times in total.
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D
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Difficulty:
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Question Stats:
49% (03:04) correct
51%
(02:29)
wrong
based on 283
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Sum of first 11 terms of an arithmetic progression is 275. Which of the following can be the sum of the first 12 terms, if the first term and the common difference are positive integers?
A. 300
B. 310
C. 316
D. 324
E. 333
A. 300
B. 310
C. 316
D. 324
E. 333
12 Oct 2018, 04:44
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For sum of first 11 terms of the progression
we can use the formula:
n/2(2a+(n-1)d)
which will give us the value
50=2a+10d
also sum of progression is:
n/2[first term + nth term)
by that:
a1+a11=50
since it is mentioned in the question that the difference common difference d and the first term should be an integer then we can conclude that a1=5 and a11= 45 and the common difference d= 4 so the next term ie. a12 should be 49 so our answer here is 275+49=324
answer choice : D
Sent from my iPhone using GMAT Club Forum mobile app
we can use the formula:
n/2(2a+(n-1)d)
which will give us the value
50=2a+10d
also sum of progression is:
n/2[first term + nth term)
by that:
a1+a11=50
since it is mentioned in the question that the difference common difference d and the first term should be an integer then we can conclude that a1=5 and a11= 45 and the common difference d= 4 so the next term ie. a12 should be 49 so our answer here is 275+49=324
answer choice : D
Sent from my iPhone using GMAT Club Forum mobile app
13 Oct 2018, 23:32
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Since we are given, the sum of first 11 terms of an arithmetic progression is 275. We can take the first term to be 'a' and the subsequent terms with a common difference of 'd', added to the previous term in the sequence.
Hence, the terms would be {a, a+d, a+2d, ..., a+10d} when the series has 11 terms in it.
Similarly, when the series would be having 12 terms, the relevant terms would be {a, a+d, ..., a+11d}
Utilizing the formula of AP, we know sum of 'n' terms would be S = n/2 * [2a + (n-1) * d]
Substituting n = 11, we get the following.
S = 11/2 [2a + 10d] = 275
Simplifying this equation, we get the value of a+5d to be 25.
Now, since we are being asked to determine the sum of 12 terms in the series, we can represent it as the following.
(Sum of 11 terms in the series + 12th term)
So, this would be (275 + a + 11d). Since we know, the value of a + 5d is 25. We can represent it as, 300 + 6d.
Hence, we know the sum of 12 terms in the series would be more than 300 and also the common difference would be a multiple of 6 (it is also given that the common difference is a positive integer).
Reviewing the answer choices given, the answer would be 'D'.
Hence, the terms would be {a, a+d, a+2d, ..., a+10d} when the series has 11 terms in it.
Similarly, when the series would be having 12 terms, the relevant terms would be {a, a+d, ..., a+11d}
Utilizing the formula of AP, we know sum of 'n' terms would be S = n/2 * [2a + (n-1) * d]
Substituting n = 11, we get the following.
S = 11/2 [2a + 10d] = 275
Simplifying this equation, we get the value of a+5d to be 25.
Now, since we are being asked to determine the sum of 12 terms in the series, we can represent it as the following.
(Sum of 11 terms in the series + 12th term)
So, this would be (275 + a + 11d). Since we know, the value of a + 5d is 25. We can represent it as, 300 + 6d.
Hence, we know the sum of 12 terms in the series would be more than 300 and also the common difference would be a multiple of 6 (it is also given that the common difference is a positive integer).
Reviewing the answer choices given, the answer would be 'D'.
