Notice that the differences between terms do form an arithmetic sequence: \(2, 3, 4, 5, 6,\ldots\text{.}\) This means that the \(n\)th term of the sequence \((T_n)\) is the sum of the first \(n\) terms in the sequence \(1,2,3,4,5,\ldots\text{.}\) We say that \((T_n)\) is the sequence of partial sums of the sequence \(1,2,3,\ldots\) (partial sums because we are not taking the sum of all infinitely many terms).
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