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If the 5th and 13th number of an A.P. has there sum as zero, find the 9th number of the series.1. 12. 03. -14. Cannot be determined |
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Answer» Correct Answer - Option 2 : 0 Concept: The nth number in A.P. series = a + (n-1)d The sum of the n numbers in A.P. series = \(\rm {n\over2}\left[2a + (n-1)d\right]\) Where 'a' is the first number of the series and 'd' is the common difference Calculation: Let the first element of A.P. is 'a' and common difference is 'd' The 5th number of A.P. (a5) = a + 4d The 13th number of A.P. (a13) = a + 12d Given a5 + a13 = 0 a + 4d + a + 12d = 0 2a + 16d = 0 a + 8d = 0 a9 = 0
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