f(2) = 8
f(3) = 14
f(4) = 20
Explanation:[tex]\begin{gathered} \text{From the table, we can deduce that:} \\ To\text{ find }nthterm, \\ f(n)\text{ = f(n - 1) + 6} \\ \\ \text{When n = 1 } \\ \text{We were given value for f(1)} \\ f(1)\text{ = 1st term = 2} \end{gathered}[/tex]
This is a recursive formula as we will have to find each of term in the table using preceding term:
[tex]\begin{gathered} \text{when n = 2} \\ f(2)\text{ = f(2-1) + 6} \\ f(2)\text{ = f(1) + 6} \\ f(1)\text{ = 2 (given)} \\ f(2)\text{ = 2 + 6 = 8} \\ \text{under f(n), type 8} \end{gathered}[/tex][tex]\begin{gathered} \text{when n =3} \\ f(3)\text{ = f(3-1) + 6} \\ f(3)\text{ = f(2) + 6} \\ f2)=\text{ 8} \\ f(3)\text{ = 8 + 6 = 14} \\ \text{under f(n), type 14} \end{gathered}[/tex][tex]\begin{gathered} \text{when n = 4} \\ f(4)\text{ = f(4-1) + 6} \\ f(4)\text{ = f(3) + 6} \\ f(3)\text{ = 14} \\ f(4)\text{ = 14 + 6 = 20} \\ under\text{ }f(n),\text{ type 20} \end{gathered}[/tex]
