⁦Sequences, nth term and recurrence⁩

A متتالية ⁦is a list of numbers⁩: ⁦a₁ is the first term, a₂ the second and aₙ the nth⁩. ⁦If aₙ = ٣n − ٢, we put the term⁩'⁦s position in place of n⁩: a₄ = ٣×٤ − ٢ = ١٠.

⁦Sometimes each term is built from the one before⁩. ⁦That is a recurrence relation⁩: ⁦a₁ = ٢ and aₙ₊₁ = ٣aₙ − ١ means the next term is three times the current one, minus 1⁩. ⁦We build the terms one by one⁩.

⁦A sequence that goes up is increasing; one that goes down is decreasing⁩. ⁦One that keeps repeating the same numbers is periodic⁩: ⁦5, −5, 5, −5⁩ …

⁦The triangular numbers 1, 3, 6, 10⁩, … ⁦come from adding 1 + 2 + 3 +⁩ … . ⁦The Fibonacci sequence 1, 1, 2, 3, 5, 8⁩ … ⁦takes each term from the sum of the two before⁩.

⁦Common slips⁩: ⁦changing the sign of the constant; missing one step in a recurrence; swapping odd and even positions; confusing triangular numbers with square numbers⁩.