1. An arithmetic sequence is a sequence in which: Any term – Previous term = Constant. 2. A geometric sequence is a sequence in which:
SUMMARY Any term
____________ Previous term = Constant.
3. Formulae for arithmetic sequences and series: (a) The general term Tn of an arithmetic sequence: Tn = a + (n – 1) d Example: T27 = a + 26d Example: T48 = a + 47d
(b) A series is a sum of a sequence. (c) The sum Sn of the fi rst n terms of an arithmetic series: S n = n
(d) Notation
T1 = S1 = a = fi rst term n = the number of terms to be added d = common difference = Any term − Previous term
Tn = value of the term in the nth place Sn = sum of the fi rst n terms
4. A sequence is quadratic if the sequence of second differences is a sequence of the same constant.
