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Position-to-terms rules use algebra to work out the term if the position in the sequence is known. This is also called the nth term, which is a position-to-term rule that works out a term at position \(n\).

Write the first five terms of the sequence \(3n + 4\).

\(n\) represents the position in the sequence. The first term in the sequence is when \(n = 1\), the second term in the sequence is when \(n = 2\), and so on.

To find the terms, substitute \(n\) for the position number:

• when \(n = 1\), \(3n + 4 = 3 \times 1 + 4 = 3 + 4 = 7\)
• when \(n = 2\), \(3n + 4 = 3 \times 2 + 4 = 6 + 4 = 10\)
• when \(n = 3\), \(3n + 4 = 3 \times 3 + 4 = 9 + 4 = 13\)
• when \(n = 4\), \(3n + 4 = 3 \times 4 + 4 = 12 + 4 = 16\)
• when \(n = 5\), \(3n + 4 = 3 \times 5 + 4 = 15 + 4 = 19\)

The first five terms of the sequence: \(3n + 4\) are \(7, 10, 13, 16, 19, ...\)

When the \(nth\) term is known, it can be used to work out specific terms in a sequence. For example, the 50th term can be calculated without calculating the first 49 terms, which would take a long time.