Question

the ninth term of an ap is -32 and the sum of its 11 and 13th term is -94

Answer 1

The required AP is 8,3,-2,-7,••••••••
refer to the image attached for solution
a=first term
d=common difference

Answer 2

Hi !

9th term = a + 8d

a + 8d = -32 ---> [1]


11th term = a + 10d
13th term = a + 12d

a + 10d + a + 12d = -94

2a + 22d = -94

2 [ a + 11d ] = -94

a + 11d = -47 ------> [ 2]


(1) - (2)

a + 8d = -32
- a + 11d = -47
===========================
-3d = 15

d = -5

a - 55 = -47

a = -47 + 55

a = 8


The AP is :-

8 , 3 , -2 , -7 ...............