What is the fifth term of the sequence given that the first two terms are 2 and 3, and each subsequent term is found by adding the two preceding terms and multiplying the sum by -2?

What is the fifth term of the sequence given that the first two terms are 2 and 3, and each subsequent term is found by adding the two preceding terms and multiplying the sum by -2?

• A. A. -14
• B. B. -12
• C. C. -10
• D. D. -8

Answer: (D)

To find the fifth term of the sequence where the first two terms are 2 and 3, and each subsequent term is calculated by adding the two preceding terms and multiplying the sum by -2, we start by identifying the terms step by step. 1. The first term is 2. 2. The second term is 3. For the third term, we add the first and second terms: - Third term = (first term + second term) * -2 = (2 + 3) * -2 = 5 * -2 = -10. Next, we calculate the fourth term: - Fourth term = (second term + third term) * -2 = (3 + -10) * -2 = (-7) * -2 = 14. Now, moving on to the fifth term: - Fifth term = (third term + fourth term) * -2 = (-10 + 14) * -2 = 4 * -2 = -8. Thus, the fifth term of the sequence is -8, making it the correct answer. This systematic process of adding the preceding terms and applying the multiplication factor leads accurately to the desired term in the sequence.

To find the fifth term of the sequence where the first two terms are 2 and 3, and each subsequent term is calculated by adding the two preceding terms and multiplying the sum by -2, we start by identifying the terms step by step.

1. The first term is 2.

2. The second term is 3.

For the third term, we add the first and second terms:

• Third term = (first term + second term) * -2 = (2 + 3) * -2 = 5 * -2 = -10.

Next, we calculate the fourth term:

• Fourth term = (second term + third term) * -2 = (3 + -10) * -2 = (-7) * -2 = 14.

Now, moving on to the fifth term:

• Fifth term = (third term + fourth term) * -2 = (-10 + 14) * -2 = 4 * -2 = -8.

Thus, the fifth term of the sequence is -8, making it the correct answer. This systematic process of adding the preceding terms and applying the multiplication factor leads accurately to the desired term in the sequence.