can you check my answers please?

What are the first three terms of the sequence: a1 = 3 and an = 2(an1)2?

2, 8, 18

3, 18, 648

--3, 32, 50

2, 6, 12, 24
What is the 14th term in the sequence: an = 4n + 13?

-43

43

__> -69

69
What is the recursive rule for the sequence: −2.7, −8.3, −13.9, −19.5, −25.1 …?
(Points : 4)
an = an 1 + 5.6

an = an + 1 - 5.6

an = an + 1 + 5.6

--> an = an 1 - 5.6

Which describes the type of sequence in 99, 88, 66, 55, …?

both arithmetic and geometric

geometric

arithmetic

---> neither arithmetic nor geometric

Hello Jennifer, First off are you in K12 as well? If so I too am working on this. haha. I think #1 is correct but #2 is correct for sure if your 4n is a negative otherwise it would be just 69 not -69. the others, I am not sure of at the moment

Let's go through each question step-by-step:

1) What are the first three terms of the sequence: a1 = 3 and an = 2(an-1)^2?

To find the first three terms of the sequence, we can use the recursive rule given. Let's calculate step-by-step:

a1 = 3 (given)
a2 = 2(a1)^2 = 2(3)^2 = 2(9) = 18
a3 = 2(a2)^2 = 2(18)^2 = 2(324) = 648

Therefore, the first three terms of the sequence are 3, 18, and 648.

2) What is the 14th term in the sequence: an = 4n + 13?

To find the 14th term in the sequence, we can plug in n = 14 into the given equation:

a14 = 4(14) + 13 = 56 + 13 = 69

Therefore, the 14th term in the sequence is 69.

3) What is the recursive rule for the sequence: −2.7, −8.3, −13.9, −19.5, −25.1 …?

To determine the recursive rule for the sequence, we need to identify the pattern between consecutive terms. Let's calculate the differences between each term:

-8.3 - (-2.7) = -5.6
-13.9 - (-8.3) = -5.6
-19.5 - (-13.9) = -5.6
-25.1 - (-19.5) = -5.6

We observe that the difference between consecutive terms is constant and equal to -5.6. Therefore, the recursive rule for the sequence is:

an = an-1 - 5.6

4) Which describes the type of sequence in 99, 88, 66, 55, …?

To determine the type of sequence, we need to examine the differences between consecutive terms. Let's calculate the differences:

88 - 99 = -11
66 - 88 = -22
55 - 66 = -11

The differences between consecutive terms are not constant, indicating that the sequence is neither arithmetic nor geometric.

Therefore, the correct answer is "neither arithmetic nor geometric."

Please note that while I have provided step-by-step explanations, it is always important to double-check your answers to ensure accuracy.

Sure, let's go through each question and check your answers:

1. What are the first three terms of the sequence: a1 = 3 and an = 2(an-1)^2?

To find the terms of the sequence, we can plug in the given values into the formula and calculate each term. Starting with a1 = 3:

a1 = 3
a2 = 2(a1)^2 = 2(3)^2 = 2(9) = 18
a3 = 2(a2)^2 = 2(18)^2 = 2(324) = 648

So the correct answer is option (2), 3, 18, 648.

2. What is the 14th term in the sequence: an = 4n + 13?

To find the 14th term, we can substitute n = 14 into the given formula and calculate the value:

a14 = 4(14) + 13 = 56 + 13 = 69

So the correct answer is option (4), 69.

3. What is the recursive rule for the sequence: −2.7, −8.3, −13.9, −19.5, −25.1 …?

The recursive rule describes how to obtain each term of the sequence from the previous term. To find the recursive rule for this sequence, we need to identify the pattern between each term:

-2.7 to -8.3 is -2.7 - 5.6
-8.3 to -13.9 is -8.3 - 5.6
-13.9 to -19.5 is -13.9 - 5.6
-19.5 to -25.1 is -19.5 - 5.6

We can see that each term is obtained by subtracting 5.6 from the previous term. Therefore, the correct answer is option (4), an = an-1 - 5.6.

4. Which describes the type of sequence in 99, 88, 66, 55, …?

To determine the type of sequence, we should look for a pattern between each term. In this case, we can observe that each term is decreasing by 11 and then decreasing by 9. This pattern continues, with each term alternating between subtracting 11 and subtracting 9. Since the difference between terms is not constant, this sequence is neither arithmetic nor geometric.

Therefore, the correct answer is option (4), neither arithmetic nor geometric.

I hope this helps! Let me know if you have any further questions.