Question

If twice the 11^th term of an A.P is equal to 7 times of its 21^st terms, then the value of 25^th term is ___________.

Answer 1

Let us suppose a denote the first term of A.P and d represents the common difference
Then 11^th term is a + 10d
21^st term is a + 20d
According to given condition,
2(11^th term) = 7(21^st 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 25^th term of A.P is 0.