For the sequence 2, 4, 6, 8, 10......
You can observe that the common difference is 2
[tex]T_2-T_1\text{ = 4 - 2 = 2}[/tex][tex]f(0)\text{ = 2}[/tex]Since we already know that the common difference is 2, the recursive formula can be written generally as :
[tex]f(x)\text{ = }f(x-1)\text{ + 2}[/tex]Where f(x) is the present term and f(x-1) is the preceding term
The equation written above is the linear equation in the recursive form.
For the explicit form of the linear equation
Since the common difference, d = 2. It is obvious that the equation is an AP
The general formula for an arithmetic progression is:
[tex]T_n\text{ = }a\text{ + (n - 1)d}[/tex]The first value, a = 2
The common diference, d = 2
The explicit form of the linear equation then becomes:
[tex]T_n=\text{ }2\text{ + }(n\text{ - 1) }2[/tex]Where n is the number of terms in the sequence
