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.

Question

Philoid · Accepted Answer

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 = - 57 ……..(2)

Subtracting equation (1) from equation (2), we get,

3d = - 15

⇒ d = - 5

∴ Common difference = d = - 5