Question

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

Options

• 0

• 40

• 20

• 2 × (30 + 10)

Answer 1

Ten times the 10th term of an A.P. is equal to twenty times the 20th term of the same A.P. The 30th term of this A.P. is 0.

Explanation:

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

10T₁₀ = 20T₂₀

`\implies` 10(a + 9d) = 20(a + 19d)

`\implies` a + 9d = 2(a + 19d)

`\implies` a + 9d = 2a + 38d

`\implies` a + 29d = 0

`\implies` T₃₀ = 0