The sequence given is \( (1, 2), (2, 4), (3, 6), (4, 8), (5, 10), (6, 12) \). These pairs can be interpreted as points \((n, 2n)\), where \(n\) is the term number.
To find an explicit formula for this sequence, we can observe that the second value in each pair is simply twice the first value. Therefore, we can express the sequence in terms of \(n\):
\[ a_n = 2n \]
where \(a_n\) is the \(n\)-th term of the sequence.
To find the 100th term, we can plug \(n = 100\) into our formula:
\[ a_{100} = 2 \cdot 100 = 200 \]
Thus, the explicit formula for the sequence is \(a_n = 2n\) and the 100th term of the sequence is \(200\).
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