Question

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 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,

a₁₁ + a₁₃ = –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.