(A₁)

AP is 2, - 2, - 6, - 10, ….

So common difference is simply

a₂ - a₁ = - 2 - 2 = - 4 = (B₃)

(A₂)

Given

First term, a = - 18

No of terms, n = 10

Last term, a_n = 0

By using the nth term formula

a_{n =} a + (n - 1)d

0 = - 18 + (10 - 1)d

18 = 9d

d = 2 = (B₅)

(A₃)

Given

First term, a = 0

Tenth term, a₁₀ = 6

By using the nth term formula

a_{n =} a + (n - 1)d

a₁₀ = a + 9d

6 = 0 + 9d

= (B₆)

(A₄)

Let the first term be a and common difference be d

Given that

a₂ = 13

a₄ = 3

a₂ - a₄ = 10

a + d - (a + 3d) = 10

d - 3d = 10

- 2d = 10

d = - 5

= (B₁)