If 9 times the 9th term of an A.P. is equal to 13 times the 13th term,

Question:

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

(a) 0

(b) 22

(c) 220

(d) 198

Solution:

Let a denote the first term of A.P and denote the common difference of the A.P

Then ninth term is a + 8d and 13th term is + 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 = – 21d

i.e + 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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