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)

1st

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9th

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12th

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None of these

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Solution

The correct option is C 12th
(c) T_n = a + (n - 1)d. Hence we get 3^rd + 5^th term = (a + 2d) + (a + 4d) = 2a + 6d. Similarly, 6, 11 and 13^th terms = (a + 5d) + (a + 10d) + (a + 12d) = 3a + 27d. Now 2a + 6d = 3a + 27d, hence a + 11d = 10. This means that 12^th term is zero.

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