In the following series what is the nth term: 1, 1, 2, 3, 5, 8, 13...
The series provided has the terms 1, 1, 2, 3, 5, 8, 13 ... It can be seen that the nth term `T_n` is the sum of the two preceding terms. Or `T_n = T_(n - 1) + T_(n - 2)` . Of course, this applies only from the 3rd term as to determine any term two prior terms are required.
The series provided is called the Fibonacci series and the first two terms of this series are 0 and 1. The nth term of the series can also be written as `T_n = ((C1)^n - (C2)^n)/sqrt 5` where `C1 = (1+sqrt 5)/2` and `C2 = (1 - sqrt 5)/2` . It should be noticed that both C1 and C2 are irrational numbers; and this does not allow the integer `T_n` to be estimated exactly using the formula.