The Fibonacci series starts with 1, 1, 2, 3, 5, 8, ... Each number is the sum of the previous two numbers. You can easily continue adding (you might put a formula in Excel, and copy it), but you quickly reach very, very large numbers - long before the 10,000th. term.
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1, 1 and 2
Leonardo Fibonacci first recorded his sequence in his book Liber Abaci, which was published in 1202.
1, 1, 2, 3, 5, 8
If the first two numbers are 0, 1 or -1 (not both zero) then you get an alternating Fibonacci sequence.
The Fibonacci sequence starts with 1 and 1. However any sequence in which the first two terms are given and the rest are defined recursively as t(n) = t(n-2) + t(n-1), with n = 3, 4, ... is also known as a Fibonacci sequence. Note the "the" and "a" preceding Fibonacci sequence.