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

Question

Responses

Multiply by the common ration of -3.5
Multiply by the common ration of -3.5

Add the common difference of -3.5
Add the common difference of -3.5

Add the common ratio of -3.5
Add the common ratio of -3.5

Multiply by the common difference of -3.5

Classify the following list of numbers as an arithmetic sequence, a geometric sequence, or neither.

9, 4, -1, -6

(1 point)
Responses

Neither
Neither

Geometric
Geometric

Arithmetic
Arithmetic

Not enough information given

What is the common ratio in the following geometric sequence?

2, 1/2,1/8,1/32...


(1 point)
Responses

-1.5
-1.5

1/4
1 fourth

1/2
1 half

4

Given the first five terms of the sequence 19, 15, 11, 7, 3... use the subscript notation to describe a7
.(1 point)
Responses

a7=−5
A sub 7 is equal to negative 5

a7=−9
A sub 7 is equal to negative 9

a7=−1
A sub 7 is equal to negative 1

a7=−4

Given the first five terms of the sequence 81, 27, 9, 3, 1, 13
... use the subscript notation to describe a7
.(1 point)
Responses

a7=27
A sub 7 is equal to 27

a7=19
A sub 7 is equal to 1 ninth

a7=3
A sub 7 is equal to 3

a7=127

Answer 1

1. For the sequence 23, 19.5, 16, 12.5, the terms are decreasing. The difference between successive terms is -3.5. Therefore, the correct option is: Add the common difference of -3.5.

2. The sequence 9, 4, -1, -6 shows a consistent difference of -5 between terms:

   • 9 to 4: -5
   • 4 to -1: -5
   • -1 to -6: -5 Therefore, this is an arithmetic sequence. The correct option is: Arithmetic.

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

   • 1/2 ÷ 2 = 1/4
   • 1/8 ÷ 1/2 = 1/4
   • 1/32 ÷ 1/8 = 1/4 The common ratio is 1/4. Therefore, the correct option is: 1/4.

4. The sequence 19, 15, 11, 7, 3 has a common difference of -4. Therefore, to find a_7:

   • a_6 = 3 - 4 = -1
   • a_7 = -1 - 4 = -5 Thus, a_7 is: a7=−5.

5. The sequence 81, 27, 9, 3, 1, ..., is a geometric sequence where each term is being divided by 3. To find a_7:

   • a_6 = 1
   • a_7 = 1/3 Therefore, a_7 can be expressed as: a7=1/3.

Please note that there seems to be a typo in your last sequence response regarding a_7. It should denote the correct geometric progression rather than giving an incorrect option like 127. Always check the initial terms to deduce the pattern.