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13 Nov 2023, 02:30
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B
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Difficulty:
95%
(hard)
Question Stats:
45% (02:33) correct
55%
(02:17)
wrong
based on 133
sessions
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If the sum of the 6th, 11th and 30th terms of an arithmetic progression is equal to the sum of the 3rd, 8th, 18th and the 25th terms, then the sum of the first how many terms of the series is zero?
A. 15
B. 13
C. 12
D. 11
E. 7
A. 15
B. 13
C. 12
D. 11
E. 7
Updated on: 13 Nov 2023, 04:57
Originally posted by VibhuAnurag on 13 Nov 2023, 03:55.
Last edited by VibhuAnurag on 13 Nov 2023, 04:57, edited 1 time in total.
Last edited by VibhuAnurag on 13 Nov 2023, 04:57, edited 1 time in total.
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Option B.
nth term of an A.P. = a + d(n - 1)
--> (a + 5d) + (a + 10d) + (a + 29d) = (a + 2d) + (a + 7d) + (a + 17d) + (a + 24d)
--> 3a + 44d = 4a + 50d
--> a + 6d = 0
Since a + 6d represents the 7th term of the sequence, this means that the 7th term is 0. Therefore, since this is an A.P., there must be an equal number of terms to the left and right of zero for the sum of the numbers to be equal to zero. Hence, there must be 13 terms, as there will be 6 terms to the left and 6 terms to the right of 0.
nth term of an A.P. = a + d(n - 1)
--> (a + 5d) + (a + 10d) + (a + 29d) = (a + 2d) + (a + 7d) + (a + 17d) + (a + 24d)
--> 3a + 44d = 4a + 50d
--> a + 6d = 0
Since a + 6d represents the 7th term of the sequence, this means that the 7th term is 0. Therefore, since this is an A.P., there must be an equal number of terms to the left and right of zero for the sum of the numbers to be equal to zero. Hence, there must be 13 terms, as there will be 6 terms to the left and 6 terms to the right of 0.
