Question
The sum of 3rd and 15th elements of an arithmetic expression is equal to the sum of 6th, 11th and 13th elements of the progression. Then which element of the series should necessarily be equal to zero(CAT 2003)
Answer: Option C
:
C
(c) Tn = a + (n - 1)d. Hence we get 3rd + 5th term = (a + 2d) + (a + 4d) = 2a + 6d. Similarly, 6, 11 and 13th terms = (a + 5d) + (a + 10d) + (a + 12d) = 3a + 27d. Now 2a + 6d = 3a + 27d, hence a + 11d = 10. This means that 12th term is zero.
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:
C
(c) Tn = a + (n - 1)d. Hence we get 3rd + 5th term = (a + 2d) + (a + 4d) = 2a + 6d. Similarly, 6, 11 and 13th terms = (a + 5d) + (a + 10d) + (a + 12d) = 3a + 27d. Now 2a + 6d = 3a + 27d, hence a + 11d = 10. This means that 12th term is zero.
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