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Class 10 > Learn Mathematics > In a certain A.P the 24th term is twice the 10th term....
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In a certain A.P the 24th term is twice the 10th term. Prove that the 72nd term is twice the 34th term?

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Let the first term be a and the common difference be b. So, by the given condition:- t24=2 x t10 --> a + 23 b = 2 ( a + 9b) = 2a + 18b. This gives: a = 5b. So, the 72nd term: t72 = a +71b = 5b + 71b = 76b. and the 34th term: t34 = a + 33b = 5b + 33b = 38b = 76b/2 = t72/2. So, the 72nd term is twice...
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Let the first term be a and the common difference be b. So, by the given condition:- t24=2 x t10 --> a + 23 b = 2 ( a + 9b) = 2a + 18b. This gives: a = 5b. So, the 72nd term: t72 = a +71b = 5b + 71b = 76b. and the 34th term: t34 = a + 33b = 5b + 33b = 38b = 76b/2 = t72/2. So, the 72nd term is twice the 34th term. (Proved) read less
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