Question

If 100 times the 100^th term of an A.P. with non zero common difference equals the 50 times its 50^th term, then the 150th term of this A.P. is ______.

Options

• – 150

• 150 times its 50^th term

• 150

• Zero

Answer 1

If 100 times the 100^th term of an A.P. with non zero common difference equals the 50 times its 50^th term, then the 150th term of this A.P. is zero.

Explanation:

Let 'a' is the first term and 'd' is the common difference of an A.P.

Now, According to the question

100a₁₀₀ = 50a₅₀

⇒ 100(a + 99d) = 50(a + 49d)

⇒ 2a + 198d = a + 49d

⇒ a + 149d = 0

Hence, T₁₅₀ = a + 149d = 0