Find the indicated terms in each of the following A.P.s :

(i) 1, 6, 11, 16, ….; a₂₀

(ii) -4, -7, -10, -13, …., a₂₅, a_n

(i) The given list of numbers is 1, 6, 11, 16, …

Here, a₂ - a₁ = 6 - 1 = 5,     a₃ - a₂ = 11 - 6 = 5,

          a₄ - a₃ = 16 - 11 = 5

i.e. any term - preceding term = 5, a fixed number.
So, the given list of numbers forms an A.P. with a = 1 and d = 5.

∴ nth term = a_n = a + (n - 1)d = 1 + (n - 1)5 = 1 + 5n - 5 = 5n - 4.

Putting n = 20, we get
a₂₀ = 5 × 20 - 4 = 100 - 4 = 96.

Hence, a₂₀ = 96.

(ii) The given list of numbers is -4, -7, -10, -13, ….

Here, a₂ - a₁ = -7 - (-4) = -3,     a₃ - a₂ = -10 - (-7) = -3,

          a₄ - a₃ = -13 - (-10) = -3

i.e. any term - preceding term = -3, a fixed number.
So, the given list of numbers forms an A.P. with a = -4 and d = -3.

∴ nth term = a_n = a + (n - 1)d = -4 + (n - 1)(-3) = -4 - 3n + 3 = -3n - 1.

Putting n = 25, we get
a₂₅ = -3 × 25 - 1 = -75 - 1 = -76.

Hence, a₂₅ = -76 and a_n = -3n - 1.