1. Which of the following statements correctly determines the rule for generating the next term in the sequence 23, 19.5, 16, 12.5....

Question

A) Add the common ratio of -3.5
B) Multiply by the common difference of -3.5
C) Multiply by the common ration of -3.5
D) Add the common difference of -3.5

2. Classify the following list of numbers as an arithmetic sequence, a geometric sequence, or neither. 9,4,-1,-6
A) Neither
B) Geometric
C) Not enough information given
D) Arithmetic

3. What is the common ratio in the following geometric sequence 2, 1/2, 1/8, 1/32...
A) -1.5
B) 1/2
C) 1/4
D) 4

Answer 1

1. The sequence provided is 23, 19.5, 16, 12.5. To find the rule governing the sequence, we observe that the difference between consecutive terms is -3.5:

• 23 - 3.5 = 19.5
• 19.5 - 3.5 = 16
• 16 - 3.5 = 12.5

Therefore, the correct answer is: D) Add the common difference of -3.5

2. To determine whether the sequence 9, 4, -1, -6 is arithmetic, we check if the difference between consecutive terms is constant:

• 4 - 9 = -5
• -1 - 4 = -5
• -6 - (-1) = -5

Since the difference is constant, this is an arithmetic sequence. Therefore, the correct answer is: D) Arithmetic

3. In the geometric sequence 2, 1/2, 1/8, 1/32, we calculate the common ratio by dividing any term by the previous term:

• \( \frac{1/2}{2} = \frac{1}{4} \)
• \( \frac{1/8}{1/2} = \frac{1/4} \)
• \( \frac{1/32}{1/8} = \frac{1/4} \)

The common ratio is consistent and equal to \( \frac{1}{4} \). Therefore, the correct answer is: C) 1/4