1.1 Arithmetic Sequences
Terms
sequence - an ordered list of numbers or terms; e.g., 1, 2, 4, 8, 16.
term - a number in a sequence; individual terms in a sequence are represented by t1 for the first term, t4 for the fourth term, or in general, by tn for the n/superth term
general term - a formula, represented by tn, that expresses each term of a sequence as a function of its position; e.g., tn = 2n−1
series - the sum, S, of the terms in a sequence; e.g.,Sn =1+2+4+8+16+32+64.
recursion - a way of defining a sequence given the first term or terms and the method to determine each term using the preceding term or terms; e.g., t1 = 5, and tn = 2tn−1
Infinite Sequence - a list of terms that continue with no defined end point; e.g., 1, 2, 4, 8, 16, 32, 64... (the “...” indicates that the list continues with no specified end point)
arithmetic sequence - a sequence of numbers where any pair of consecutive terms have the same, or common, difference, d
Defining the General Terms
determine first whether it is an arithmetic sequence. If it is, determine the common difference