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If 4 times the 4th term of an A.P. is equal to 18 times its 18th term, then find its 22nd term. - Mathematics

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प्रश्न

If 4 times the 4th term of an A.P. is equal to 18 times its 18th term, then find its 22nd term.

बेरीज
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उत्तर

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)   ...[∵ a= 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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पाठ 11: Arithmetic Progression - Exercises 1

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