If twice the 11th term of an A.P is equal to 7 times of its 21st terms,

Let us suppose a denote the first term of A.P and d represents the common difference

Then 11th term is a + 10d

21st term is a + 20d

According to given condition,

2(11th term) = 7(21st term)

i.e 2(a + 10d) = 7(a + 20d)

i.e 2a + 20d = 7a + 140d

i. 5a + 120d = 0

i.e 5(a + 24d) = 0

Since 5 ≠ 0

⇒ a + 24d = 0

i.e 25th term of A.P is 0.