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in Arithmetic Progression by (29.9k points)
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If 4 times the 4th term of an AP is equal to 18 times its 18th term then find its 22nd term.

1 Answer

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Best answer

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

4 x a4 = 18 x a18 (Given)

\(\Rightarrow\) 4(a + 3d) = 18(a + 17d) [an = a + (n - 1)d]

\(\Rightarrow\) 2(a + 3d) = 9(a + 17d)

\(\Rightarrow\) 2a + 6d = 9a + 153d

\(\Rightarrow\) 7a = -147d

\(\Rightarrow\) a = -21d

\(\Rightarrow\) a + (22 - 1)d = 0

\(\Rightarrow\) a22 = 0

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

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