The 7th term of an AP is - 4 and its 13th term is - 16. Find the AP.

Question

Philoid · Accepted Answer

Let a be the first term and d be the common difference.

Given: a₇ = - 4

a₁₃ = - 16

Now, Consider a₇ = - 4

⇒ a + (7 - 1)d = - 4

⇒ a + 6d = - 4 ……….(1)

Consider a₁₃ = - 16

⇒ a + (13 - 1)d = - 16

⇒ a + 12d = - 16 ……….(2)

Now, subtracting equation (1) from (2), we get,

6d = - 12

⇒ d = - 2

∴ from equation (1), we get,

a = - 4 - 6d

⇒ a = - 4 - 6 × (-2)

⇒ a = - 4 + 12

⇒ a = 8

Thus the AP is a, a + d, a + 2d, a + 3d, a + 4d,….

Therefore the AP is 8, 6, 4, 2, 0,….