Question

Write the first 4 terms of the sequence defined by the recursive rule:

a. (f(1) = 3, f(n) = f(n-1) + 4, n > 1)
A. 3, 7, 11, 15
B. 3, 11, 15, 19
C. 3, 7, 15, 19
D. 3, 7, 11, 19

Answer 1

The first 4 terms of the sequence defined by the recursive rule are 3, 7, 11, 15.

Step-by-step explanation:

The sequence defined by the recursive rule is given by: f(1) = 3 and f(n) = f(n-1) + 4 for n > 1. To find the first 4 terms of the sequence, we can follow these steps:

1. Start with the first term: f(1) = 3
2. To find the second term, substitute n = 2 in the recursive rule: f(2) = f(2-1) + 4 = f(1) + 4 = 3 + 4 = 7
3. To find the third term, substitute n = 3 in the recursive rule: f(3) = f(3-1) + 4 = f(2) + 4 = 7 + 4 = 11
4. To find the fourth term, substitute n = 4 in the recursive rule: f(4) = f(4-1) + 4 = f(3) + 4 = 11 + 4 = 15

Therefore, the first 4 terms of the sequence are: 3, 7, 11, 15. The correct option is A. 3, 7, 11, 15.

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