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An explicit formula for this arithmetic sequence is given by an = a + (n −1)b, n ∈ N, a recursive formula is given by a1 = a and an = an−1 + b for n > 1. Here are some examples of arithmetic sequences, see if you can determine a and b in each case: 1, 2, 3, 4, 5, ... 2, 4, 6, 8, 10, ... 1, 4, 7, 10, 13, ...
arithmetic sequences (also known as arithmetic progressions, or simply A.P). The characteristic of such a sequence is that there is a common difference between successive terms. For example: 1, 3, 5, 7, 9, 11, . . . (the odd numbers) has a first term of 1 and a common difference of 2.
This unit introduces sequences and series, and gives some simple examples of each. It also explores particular types of sequence known as arithmetic progressions (APs) and geometric progressions (GPs), and the corresponding series.
1.5 Rules for sequences. Here are the rules your sequence friends use to make babies. Suppose (an) and (bn) are covergent sequences, that (cn) is a divergent sequence, that k is a real number, and f(x) is a continuous function de ned at all an and limn!1 an. limn!1 k = k; limn!1(kan) = k (limn!1 an);
A sequence is simply an ordered list u1, u2, u3,K, un, of numbers (or terms). This is often abbreviated to {}un. For our purposes each term un is usually given in one of two ways: (i) as a function of the preceding term(s), or (ii) as a function of its position in the sequence.
There are a number of ways to denote a sequence, some of which are more useful for specific types of sequences. One way to specify a sequence is to list the elements. For example, the first four odd numbers form the sequence (1,3,5,7). This notation can be used for infinite sequences as well.
Sequences. Sequences are just ordered lists of numbers such as this one. f1; 2; 3; 4; 5; g. We label each term with an index so we can keep track of it. We’ll call the first term a1, the second term a2, and so on. So we would notate the general n th term as an.
