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Prove that in a sequence of numbers 49,4...

Prove that in a sequence of numbers 49,4489,444889,44448889 in which every number is made by inserting 48-48 in the middle of previous as indicated, each number is the square of an integer.

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To prove that each number in the sequence \(49, 4489, 444889, 44448889\) is the square of an integer, we will derive a general formula for the \(n\)-th term of the sequence and show that it can be expressed as a perfect square. ### Step 1: Identify the pattern in the sequence The sequence starts with: - \( T_1 = 49 \) - \( T_2 = 4489 \) - \( T_3 = 444889 \) - \( T_4 = 44448889 \) ...
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Knowledge Check

  • In a certain sequence of numbers, each term after the 1 st term is the result of adding 2 to the previous term and multiplying that sum by 3 . If the 4th term in the sequence is 186 , what is the 2 nd term ?

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    D
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