~Determine whether each sequence is arithmetic or geometric fund the next three terms~

*Doing a math unit test and stuck on these five*
1.14,19,24,29....

2.-2,8,-16,32...

3.81,27,9,3...

4.What are the first four terms of an arithmetric sequence if the common diffrence is 1.5 and the first term is 15

5.What are the first four terms of a geometric sequence if the common ratio is 10 an the first term is 4.5

Thanks:)

I know this was a different test I just wanted to spread this answer across Jiskha because nobody had post the whole quiz yet.

I'm just being nice.

Sure! Let's go through each question step by step.

Question 1: Determine whether each sequence is arithmetic or geometric and find the next three terms. The given sequence is 1, 14, 19, 24,...

To determine if the sequence is arithmetic or geometric, we need to check if the difference between consecutive terms is the same (arithmetic) or if the ratio between consecutive terms is the same (geometric).

For the given sequence, let's calculate the differences between consecutive terms:
Difference between 14 and 1: 14 - 1 = 13
Difference between 19 and 14: 19 - 14 = 5
Difference between 24 and 19: 24 - 19 = 5

Since the differences are not the same, we can conclude that the sequence is not arithmetic. Now, let's calculate the ratios between consecutive terms for a geometric sequence:
Ratio between 14 and 1: 14 / 1 = 14
Ratio between 19 and 14: 19 / 14 ≈ 1.36
Ratio between 24 and 19: 24 / 19 ≈ 1.26

The ratios are not the same either, so the sequence is not geometric either. Without a clear pattern, it is challenging to find the next three terms.

Question 2: The given sequence is -2, 8, -16, 32,...

Let's follow the same steps. Calculating the differences between consecutive terms:
Difference between 8 and -2: 8 - (-2) = 10
Difference between -16 and 8: -16 - 8 = -24
Difference between 32 and -16: 32 - (-16) = 48

The differences are not the same, so it is not an arithmetic sequence. Now, let's calculate the ratios between consecutive terms for a geometric sequence:
Ratio between 8 and -2: 8 / (-2) = -4
Ratio between -16 and 8: -16 / 8 = -2
Ratio between 32 and -16: 32 / (-16) = -2

The ratios are not the same either, so it is not a geometric sequence. Consequently, finding the next three terms is also challenging without a clear pattern.

Question 3: The given sequence is 81, 27, 9, 3,...

Let's apply the same steps. Calculating the differences between consecutive terms:
Difference between 27 and 81: 27 - 81 = -54
Difference between 9 and 27: 9 - 27 = -18
Difference between 3 and 9: 3 - 9 = -6

The differences are not the same, so it is not an arithmetic sequence. Calculating the ratios between consecutive terms for a geometric sequence:

Ratio between 27 and 81: 27 / 81 = 1/3
Ratio between 9 and 27: 9 / 27 = 1/3
Ratio between 3 and 9: 3 / 9 = 1/3

The ratios are the same (1/3), so the given sequence is a geometric sequence. To find the next three terms, multiply the last term (3) by the common ratio (1/3):
- 3 * (1/3) = 1
- 1 * (1/3) = 1/3
- (1/3) * (1/3) = 1/9

Thus, the next three terms in the geometric sequence are 1, 1/3, and 1/9.

Question 4: The arithmetic sequence has a common difference of 1.5 and the first term is 15.

To find the first four terms of an arithmetic sequence, we start with the given first term (15) and add the common difference (1.5) successively.

First Term: 15
Second Term: 15 + 1.5 = 16.5
Third Term: 16.5 + 1.5 = 18
Fourth Term: 18 + 1.5 = 19.5

The first four terms of the arithmetic sequence are 15, 16.5, 18, and 19.5.

Question 5: The geometric sequence has a common ratio of 10 and the first term is 4.5.

To find the first four terms of a geometric sequence, we start with the given first term (4.5) and multiply by the common ratio (10) successively.

First Term: 4.5
Second Term: 4.5 * 10 = 45
Third Term: 45 * 10 = 450
Fourth Term: 450 * 10 = 4500

The first four terms of the geometric sequence are 4.5, 45, 450, and 4500.

I hope this explanation helps you understand how to determine whether a sequence is arithmetic or geometric and how to find the next terms based on the given information.

Lesson 3: Functions

Algebra Readiness (Pre-Algebra) B Unit 1: Functions

1. D
2. A
3. B
4. A
5. B
6. C
7. D
8. A

Written Response:
9.
Equation to see if its arithmetic:
.8-1.6 = -.8
.4-.8 = -.4 , so no it is not arithmetic

Equation to see if its geometric:
.8/1.6 = .5
.4/.8 = .5
.2/.4 = .5 , so yes the sequence is geometric

My answer is that this sequence is geometric because as you can see from above when tested, it did not turn out as arithmetic. So, then I tested to see if the sequence was geometric, and it turned out right. Meaning the answer could not be neither nor arithmetic. SO it is geometric.
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REMEMBER THE TEACHERS CAN ALWAYS CHANGE THE ORDER OF THE QUESTIONS OR THE QUESTIONS IN GENERAL. THEY CAN ALSO CHANGE THE ANSWERS.

BUT AS FOR NOW, THESE ANSWERS WILL GET YOU A 9/9 100%
YOUR WELCOME, HAVE A NICE NIGHT OR DAY =)

if the difference is constant, it's arithmetic. If the ratio is constant, it's geometric.

#1 is clearly arithmetic
#2 is geometric
#3 is too

#4 15 + 1.5 + 1.5 ...
#5 4.5 * 10 * 10 ...