Let a be the first term and d be the common difference of an AP.
nth term = an = a + (n – 1)d
Given: 9th term of an AP is -32 and the sum of its 11th and 13th terms is -94
Now,
a9 = a + 8d = -32 …(1)
a11 = a + 10d
a13 = a + 12d
Sum of 11th and 13th terms:
a11 + a13 = a + 10d + a + 12d
-94 = 2a + 22d
or a + 11d =-47 …(2)
Subtracting (1) from (2) , we have
3d = -47 + 32 = -15
or d = -5
Common difference is -5.