Question

determine the first 3 terms of the following sequence.
f(1) = -3
f(n) = 3·f(n - 1)
-3, -9, -27
-3, 6,9
-3, -6, -9
-3, 9, 27

Explanation:

Step1: Find the first term

Given \( f(1) = -3 \), so the first term is \(-3\).

Step2: Find the second term

Use the recursive formula \( f(n) = 3 \cdot f(n - 1) \). For \( n = 2 \), we have \( f(2) = 3 \cdot f(2 - 1) = 3 \cdot f(1) \). Substitute \( f(1) = -3 \), we get \( f(2) = 3 \times (-3) = -9 \).

Step3: Find the third term

For \( n = 3 \), use the recursive formula \( f(3) = 3 \cdot f(3 - 1) = 3 \cdot f(2) \). Substitute \( f(2) = -9 \), we get \( f(3) = 3 \times (-9) = -27 \).

Answer:

-3, -9, -27