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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. [CBSE 2012]

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Solution

Let a be the first term and d be the common difference of the AP. Then,

4×a4=18×a18 (Given)
4a+3d=18a+17d an=a+n-1d2a+3d=9a+17d2a+6d=9a+153d7a=-147d
a=-21da+21d=0a+22-1d=0a22=0

Hence, the 22nd term of the AP is 0.

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