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Question
If six times of the 3rd term is equal to the eight times of 7th term in an A.P., then what will be the 19th term?
Solution
Let a be the first term and d be the common difference.
Then, according to the question,
6a3 = 8a7
⇒ 6(a + 2d) = 8(a + 6d)
⇒ 6a + 12d = 8a + 48d
⇒ 6a – 8a = 48d – 12d
⇒ – 2a = 36d
⇒ a = – 18d
Now, a19 = a + 18d = (– 18d) + 18d = 0
Hence, the 19th term of the A.P. is 0.
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