Answer:
The correct answer is f(n) = f(n − 1) + 4
Step-by-step explanation:
Let us consider the sequence: 4, 8, 12, …
Using f(n) = f(n − 1) + 4, we can easily get the sequence.
As the first term is 4 and next term is obtained by adding 4 to the first term.
i.e. 4+4 = 8
8+4 = 12
12+4 = 16 and so on.
Since the next term is obtained by adding 4 to the previous term.
<em>So, f(n) = f(n-1) + 4 would be the correct recursive formula for the function of the sequence 4, 8, 12, .... </em>
<em>Verification: </em>
<em> f(n) = f(n-1) + 4</em>
Putting n=2 in f(n) = f(n-1) + 4 to get the second term of the sequence.
<em> f(2) = f(2-1) + 4</em>
<em> f(2) = f(1) + 4</em>
<em> f(2) = 4 + 4</em>
<em> f(2) = 8</em>
Putting n=3 in f(n) = f(n-1) + 4 to get the third term of the sequence.
<em> f(3) = f(3-1) + 4</em>
<em> f(3) = f(2) + 4</em>
<em>So, adding 4 in f(2)=8 would give us the next term i.e. 12</em>
<em> f(3) = 8 + 4</em>
<em> f(3) = 12</em>
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Keywords: recursive formula, sequence
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