If 9 times the 9th term of an A.P. is equal to 13 times the 13th term, then the 22nd term of the A.P. is
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 13th 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 22nd term of A.P.
∴ The 22nd term of the A.P is 0
Hence, the correct answer is option A.
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