# 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.

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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