Definition
Position-to-term rule
A position-to-term rule gives any sequence term directly from its position number.
What it means
Put the position number into the rule and it gives the term at that place. This is useful for far-away positions because you do not need to walk through the sequence one term at a time. Unless a task says otherwise, the first position is 1.
Remember it
Position in; term out.
Example
The sequence 5, 9, 13, 17, … has position-to-term rule 4n + 1, where n is the position. At position 12, 4 × 12 + 1 = 49, so the 12th term is 49.
Watch for
The starting position matters. A rule written for positions 1, 2, 3, … may need to change if a sequence is indexed from 0.
Common mix-up
A term-to-term rule moves from earlier terms to later ones; a position-to-term rule goes straight from a position to its term.
Exact meaning
A position-to-term rule maps each valid position number to the value of the term at that position, without requiring all earlier terms to be generated.