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The sequence 11, 21, 35, 53, 75, 101 can be analyzed to find a pattern in the differences between consecutive terms: 10, 14, 18, 22, 26. The differences themselves increase by 4 each time, indicating a quadratic relationship. The nth term can be expressed by the formula ( a_n = 3n^2 + 8n ), where ( n ) is the term number starting from 1. For example, for ( n = 1 ), ( a_1 = 11 ), and for ( n = 2 ), ( a_2 = 21 ).

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