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Question
If 4 times the 4th term of an A.P. is equal to 18 times its 18th term, then find its 22nd term.
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Solution
Let a be the first term and d be the common difference of the A.P.
Then, 4 × a4 = 18 × a18 ...(Given)
⇒ 4(a + 3d) = 18(a + 17d) ...[∵ an = a + (n – 1)d]
⇒ 2(a + 3d) = 9(a + 17d)
⇒ 2a + 6d = 9a + 153d
⇒ 7a = –147d
⇒ a = –21d
⇒ a + 21d = 0
⇒ a + (22 – 1)d = 0
⇒ a22 = 0
Hence, the 22nd term of the A.P. is 0.
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