Question

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

Answer 1

Let a be the first term and d be the common difference of the AP. Then, 

a₉  = - 32

⇒ a +(9-1) d= -32                         [a_n  = a + (n-1) d]

⇒ a + 8d = -32               ............(1)

Now ,
`a_11 + a_13 = -94`                   (Given)

`⇒ ( a +10d ) +( a + 12d) = -94`

⇒ 2a + 22d = -94

⇒ a+ 11d = -47              ...............(2)

From (1) and (2), we get

-32 -8d + 11d=-47

 ⇒ 3d = -47 + 32 =-15

⇒ d = -5 

Hence, the common difference of the AP is - 5.