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Prove that the squares of all the terms of the arithmetic sequence 4,7,10....belong to the sequence |
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Answer» Answer: Step-by-step explanation: prove that the squares of all the terms of the arithmetic sequence 4,7,10....BELONG to the sequence AP is 4 , 7 , 10 .... a = 4 d = 3 NTH term = a +(n-1)d = 4 + (n-1)3 = 4 + 3n - 3 = 3n + 1 square of nth Term = (3n + 1)² = 9n² + 6N + 1 = 3(3n² + 2n) + 1 3n² + 2n = k = 3k + 1 square of nth Term = kth Term where k = 3n² + 2n Hence proved that the squares of all the terms of the arithmetic sequence 4,7,10....belong to the sequence |
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