Q. 305.0( 10 Votes )

The 9th term of an AP is - 32 and the sum of its 11th and 13th terms is - 94. Find the common difference of the AP.

Answer :

Let a be the first term and d be the common difference.

Given: a9 = - 32


a11 + a13 = - 94


To find: common difference = d


Now, Consider a9 = - 32


a + (9 - 1)d = - 32


a + 8d = - 32 ……….(1)


Consider a11 + a13 = - 94


a + (11 - 1)d + a + (13 - 1)d = - 94


2a + 22d = - 94


a + 11d = - 47 ……..(2)


Subtracting equation (1) from equation (2), we get,


3d = - 15


d = - 5


Common difference = d = - 5

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