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Question
If 4 times the 4th term of an AP is equal to 18 times its 18th term then find its 22nd term.
Solution
Let a be the first term and d be the common difference of the AP. Then,
`4 xx a_4 = 18 xx a_18 ` (Given ) n
⇒ 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 AP is 0.
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