Question

Find an explicit formula (in terms of $n \in N$ ) for $f(n) = \left( {n - 1} \right) + 2n - 1$.

Answer 1

The explicit form of a function is just the simplified form of a given function. Here the function is $f(n) = n - 1 + 2n - 1$. Simplifying this we get the explicit form of the function.

Complete step by step solution:
The explicit formula is nothing other than a mathematical expression with a finite number of well known functions.
In other words the explicit form is nothing other than the simplified form of a given function
Here the function given is $f(n) = \left( {n - 1} \right) + 2n - 1$
In order to find the explicit form we get
$\Rightarrow f(n) = \left( {n - 1} \right) + 2n - 1 \\\ \Rightarrow f(n) = n - 1 + 2n - 1 \\\ \Rightarrow f(n) = n + 2n - 1 - 1 \\\ \Rightarrow f(n) = 3n - 2 \\\$
Therefore we obtained the explicit form of the given function .

Note:
Explicit means exact or definite. The formula is explicit because as long as it's applied correctly, the nth term can be determined. Arithmetic and geometric sequences have different explicit formulas.