3. What are the first five terms of the recursive sequence? $$ a_{n}=3 a_{n-1}-6 $$ where $$ a_{1}=7 $$

Question

UpStudy AI · Accepted Answer

1. We are given the recursive formula  
   $$
   a_{n} = 3a_{n-1} - 6
   $$  
   with the initial term:  
   $$
   a_{1} = 7.
   $$

2. **Second term:**  
   $$
   a_{2} = 3a_{1} - 6 = 3 \times 7 - 6 = 21 - 6 = 15.
   $$

3. **Third term:**  
   $$
   a_{3} = 3a_{2} - 6 = 3 \times 15 - 6 = 45 - 6 = 39.
   $$

4. **Fourth term:**  
   $$
   a_{4} = 3a_{3} - 6 = 3 \times 39 - 6 = 117 - 6 = 111.
   $$

5. **Fifth term:**  
   $$
   a_{5} = 3a_{4} - 6 = 3 \times 111 - 6 = 333 - 6 = 327.
   $$

Thus, the first five terms of the sequence are:

$$
7,\ 15,\ 39,\ 111,\ 327.
$$
The first five terms of the sequence are 7, 15, 39, 111, and 327.

What are the first five terms of the recursive sequence?

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