Knowledge Node - Sequences
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| Definition. A sequence, unlike a set, is an
ordered, countable collection of values. Basically, a sequence is a function mapped
from the natural numbers to the real numbers. A sequence is denoted as {an} Ex. Here are some example sequences. By themselves they aren't that interesting, but as always, there's more to study... The Harmonic Sequence: (an)n = (1/n)n = ( 1, 1/2, 1/3, 1/4, 1/5, ... ) Reciprocal Squares: (an)n = (1/(n2))n = ( 1, 1/4, 1/9, 1/16, ... ) Geometric Sequence (an)n = (a/(rn))n = ( a, a/r, a/r2, a/r3, ... ) I always thought it was important for a sequence to start at index 1, but apparently, the geometric sequence starts at 0. I'm sure others can start at 2, or any number you want for that matter. |
= (an)n = (an) , where n is the nth
term in the sequence.just curious... added 5/4/04