Find the middle term of the AP 10, 7, 4, ..., (-62).

First term of the AP = 10

Common difference = d = 7 - 10 = - 3

Last term = - 62

Since

a_n = a + (n - 1) × d

∴ - 62 = 10 + (n - 1) × (-3)

⇒ - 62 - 10 = - 3n + 3

⇒ - 72 = - 3n + 3

⇒ - 72 - 3 = - 3n

⇒ 3n = 75

⇒ n = 75/3 = 25

∴ Middle term is (25 + 1)/2 = 13^th

So, a₁₃ = a + (13 - 1) × d

∴ a₁₃ = 10 + 12 × (-3)

⇒ a₁₃ = 10 - 36 = - 26

∴ Middle term of the AP is - 26.