1.

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

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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