Option D is correct. The correct option for the recursive formula is [tex]f(0) =6;f(n)=f(n - 1)+4[/tex]
Given the sequence 10, 14, 18...
The first term is 10, hence
a1 = 10
The previous terms will be [tex]a_{n-1}[/tex]
From the sequence, we can see that 4 is being added to the previous term to get the next term. Hence the nth term will be expressed as:
[tex]a_n = a_{n-1} + 4[/tex]
Get the term before the first term [tex]a_0[/tex]
If n = 1
[tex]a_1 = a_{1-1} + 4\\a_1 = a_{0} + 4\\a_0=a_1-4\\a_0=10-4\\a_0=6[/tex]
Hence the correct option for the recursive formula is [tex]f(0) =6;f(n)=f(n - 1)+4[/tex]
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