Question

If 9 times the 9^th term of an A.P. is equal to 13 times the 13th term, then the 22^nd term of the A.P. is
(a) 0
(b) 22
(c) 220
(d) 198

Answer 1

Let a denote the first term of A.P and d denote the common difference of the A.P
Then ninth term is a + 8d and 13^th term is a + 12d
According to given condition,
9(a + 8d) = 13(a + 12d)
i.e 9a + 72d = 13a + 156d
i.e –156d + 72d = 4a
i.e –84d = 4a
i.e a = – 21d
i.e a + 21d = 0
which represents 22^nd term of A.P.
∴ The 22^nd term of the A.P is 0
Hence, the correct answer is option A.