Answer:
f(n) = 2n - 2
Step-by-step explanation:
Given the recursive formula
f(n) = f(n - 1) + 2 with f(1) = 0, then
f(2) = f(1) + 2 = 0 + 2 = 2
f(3) = f(2) + 2 = 2 + 2 = 4
f(4) = f(3) + 2 = 4 + 2 = 6
The terms of the sequence are 0, 2, 4, 6, ....
These are the first 4 terms of an arithmetic sequence with explicit formula
f(n) = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here d = 2 - 0 = 4 - 2 = 6 - 4 = 2 and a₁ = 0, thus
f(n) = 0 + 2(n - 1), that is
f(n) = 2n - 2 ← explicit formula
![\bf \textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh~~ \begin{cases} b=base\\ h=height\\ \cline{1-1} A=56 \end{cases}\implies 56=\cfrac{1}{2}bh\implies 112=bh \\\\\\ \boxed{112=2\cdot 2\cdot 2\cdot 2\cdot 7}\to \begin{cases} 16\cdot 7\\ 8\cdot 14\\ 4\cdot 28\\ 2\cdot 56 \end{cases}\qquad or\qquad \begin{cases} 7 \cdot 16\\ 14 \cdot 8\\ 28 \cdot 4\\ 56 \cdot 2 \end{cases}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Barea%20of%20a%20triangle%7D%5C%5C%5C%5C%20A%3D%5Ccfrac%7B1%7D%7B2%7Dbh~~%20%5Cbegin%7Bcases%7D%20b%3Dbase%5C%5C%20h%3Dheight%5C%5C%20%5Ccline%7B1-1%7D%20A%3D56%20%5Cend%7Bcases%7D%5Cimplies%2056%3D%5Ccfrac%7B1%7D%7B2%7Dbh%5Cimplies%20112%3Dbh%20%5C%5C%5C%5C%5C%5C%20%5Cboxed%7B112%3D2%5Ccdot%202%5Ccdot%202%5Ccdot%202%5Ccdot%207%7D%5Cto%20%5Cbegin%7Bcases%7D%2016%5Ccdot%207%5C%5C%208%5Ccdot%2014%5C%5C%204%5Ccdot%2028%5C%5C%202%5Ccdot%2056%20%5Cend%7Bcases%7D%5Cqquad%20or%5Cqquad%20%5Cbegin%7Bcases%7D%207%20%5Ccdot%2016%5C%5C%2014%20%5Ccdot%208%5C%5C%2028%20%5Ccdot%204%5C%5C%2056%20%5Ccdot%202%20%5Cend%7Bcases%7D)
so their product is 112, so tis just a matter of doing some quick prime factoring and combining the factors about.