24. In the sequence below, each term is found by finding the difference between the previous two numbers and mulitplying the result by -3 . What is the 6 th term of the sequence? (3, $$ 0,-9,-36, \ldots $$ ) (A) -81 (B) -135 (C) 45 (D) 81 (E) 135

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To find the 6th term of the sequence defined by the rule that each term is found by taking the difference between the previous two numbers and multiplying the result by -3, we can follow these steps:

1. **Identify the first few terms of the sequence:**
   - The given terms are: 
     - $$ a_1 = 3 $$
     - $$ a_2 = 0 $$
     - $$ a_3 = -9 $$
     - $$ a_4 = -36 $$

2. **Calculate the next terms using the rule:**
   - The formula for the $$ n $$-th term is:
     $$
     a_n = -3 \times (a_{n-1} - a_{n-2})
     $$

3. **Calculate the 5th term $$ a_5 $$:**
   - Using $$ a_4 $$ and $$ a_3 $$:
     $$
     a_5 = -3 \times (a_4 - a_3) = -3 \times (-36 - (-9)) = -3 \times (-36 + 9) = -3 \times (-27) = 81
     $$

4. **Calculate the 6th term $$ a_6 $$:**
   - Using $$ a_5 $$ and $$ a_4 $$:
     $$
     a_6 = -3 \times (a_5 - a_4) = -3 \times (81 - (-36)) = -3 \times (81 + 36) = -3 \times 117 = -351
     $$

Now, let's summarize the calculations for clarity:

- $$ a_5 = 81 $$
- $$ a_6 = -351 $$

However, it seems I made a mistake in the calculations for $$ a_6 $$. Let's recalculate it correctly:

1. **Calculate $$ a_5 $$ again:**
   $$
   a_5 = -3 \times (a_4 - a_3) = -3 \times (-36 - (-9)) = -3 \times (-36 + 9) = -3 \times (-27) = 81
   $$

2. **Calculate $$ a_6 $$ correctly:**
   $$
   a_6 = -3 \times (a_5 - a_4) = -3 \times (81 - (-36)) = -3 \times (81 + 36) = -3 \times 117 = -351
   $$

Thus, the 6th term of the sequence is $$ -351 $$.

However, since this value does not match any of the provided options, I will double-check the calculations for $$ a_6 $$:

1. **Recalculate $$ a_6 $$:**
   $$
   a_6 = -3 \times (81 - (-36)) = -3 \times (81 + 36) = -3 \times 117 = -351
   $$

It appears that I have made a mistake in interpreting the options. The correct answer for the 6th term is indeed $$ -351 $$, but it is not listed among the options provided.

Please verify the options or the sequence definition.
The 6th term of the sequence is -351.

24. In the sequence below, each term is found by finding the difference between the previous two numbers and mulitplying the result by -3 . What is the 6 th term of the sequence? (3, \( 0,-9,-36, \ldots \) ) (A) -81 (B) -135 (C) 45 (D) 81 (E) 135

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