Ten times the 10^th term of an A.P. is equal to twenty times the 20^th term of the same A.P. The 30^th term of this A.P. is :

1. 0

2. 40

3. 20

4. 2 × (30 + 10)

Let first term of A.P. be a and common difference be d.

By formula,

a_n = a + (n - 1)d

According to question,

⇒ 10a₁₀ = 20a₂₀

⇒ 10[a + (10 - 1)d] = 20[a + (20 - 1)d]

⇒ 10[a + 9d] = 20[a + 19d]

⇒ 10a + 90d = 20a + 380d

⇒ 20a - 10a = 90d - 380d

⇒ 10a = -290d

⇒ a = -29d.

a₃₀ = a + (30 - 1)d

= a + 29d

= -29d + 29d

= 0.

Hence, Option 1 is the correct option.