Sequence.md (725B)
1 # Sequence 2 3 U2.4.1 4 5 **Definition:** Sequences are ordered lists mapped to by the integers. 6 7 To define a sequence we can use the following notation where n is some arbitrary element: 8 9 $a_n = 2n$ 10 11 This defines the mapping from the integers to the set of all even numbers. 12 13 #### Arithmetic Sequence 14 15 An arithmetic sequence is a sequence where we start from some constant and then add d times the current value. 16 17 This can be explicitly stated as $a_n = a + dn$ where d is some constant. 18 19 #### Geometric Sequence 20 21 In a geometric sequence we multiply the initial term by the common ratio, defined as r, to the nth power. 22 23 A geometric sequence can be stated as $a_n=ar^n$ where r is some constant and n is the iteration, as always.