Find the common difference or ratio in each sequence. Write an algebraic expression for the sequence and find the next three terms.

6. 160, 40, 10, 2.5...

8. -1, 2, -4, 8....

Can you help me find the answers?

does ex stand for the algebraic expression ms sue

No, "ex" means "example".

For the algebraic expression of the first sequence, let's use the notation a1, a2, a3, ... to represent each term, where a1 = 160, a2 = 40, a3 = 10, and so on.

We can see that each term is obtained by multiplying the previous term by 1/4, or dividing by 4. Therefore, the algebraic expression for the sequence is:

a1, a2, a3, ... = 160, 40, 10, 2.5, ...
an = (a1/4^(n-1)) for n = 1, 2, 3, ...

To find the next three terms, we can use the formula:

a5 = (a1/4^4) = 2.5/4 = 0.625
a6 = (a1/4^5) = 0.625/4 = 0.15625
a7 = (a1/4^6) = 0.15625/4 = 0.0390625

Therefore, the next three terms are 0.625, 0.15625, and 0.0390625.

For the second sequence, it is not immediately clear what the common difference or ratio is. However, if we examine the pattern of positive and negative signs, we can see that each term alternates sign. Moreover, the magnitude of each term doubles from the previous term, starting from 1. Therefore, the common ratio is -2 for the even terms and 2 for the odd terms.

We can express this as two separate sequences for the even and odd terms:

Odd terms: 1, -4, 16, -64, ...
an = (-2)^(n/2-1) for n = 1, 3, 5, ...

Even terms: -1, 2, -8, 32, ...
an = 2^(n/2 - 1) for n = 2, 4, 6, ...

To find the next three terms, we can use the formulas:

Odd terms: a7 = (-2)^(3/2 - 1) = -4
a9 = (-2)^(5/2 -1) = 16
a11 = (-2)^(7/2 - 1) = -64

Even terms: a8 = 2^(4/2 - 1) = 8
a10 = 2^(6/2 - 1) = 32
a12 = 2^(8/2 - 1) = 128

Therefore, the next three terms are -4, 16, -64 for the odd terms and 8, 32, 128 for the even terms.

i need the algebraic equation to -1, 2, -4, 8, ...

For the sequence -1, 2, -4, 8, ..., we can use the notation a1, a2, a3, ... to represent each term, where a1 = -1, a2 = 2, a3 = -4, and so on.

We can see that each term is obtained by multiplying the previous term by -2, or multiplying by -2^n, where n is the position of the term in the sequence. Therefore, the algebraic expression for the sequence is:

a1, a2, a3, ... = -1, 2, -4, 8, ...
an = (-2)^(n-1) for n = 1, 2, 3, ...

To find the next three terms, we can use the formula:

a5 = (-2)^4 = 16
a6 = (-2)^5 = -32
a7 = (-2)^6 = 64

Therefore, the next three terms are 16, -32, and 64.

i need help trying to find the next 4 terms to 14-1n, 1/4n, and 23+n

Sure, here's how to find the next 4 terms for each of those sequences:

1. Sequence: 14-1n
- The first term is 14-1(1) = 13
- To find the second term, we subtract 1 again: 14-1(2) = 12
- To find the third term, we subtract 1 yet again: 14-1(3) = 11
- Continuing this pattern, we get the next four terms as follows:
- Fourth term: 10
- Fifth term: 9
- Sixth term: 8
- Seventh term: 7

Therefore, the next four terms for the sequence 14-1n are 10, 9, 8, 7.

2. Sequence: 1/4n
- The first term is 1/4(1) = 1/4
- To find the second term, we add 1/4: 1/4 + 1/4(2) = 3/8
- To find the third term, we add 1/4 again: 3/8 + 1/4(3) = 5/8
- Continuing this pattern, we get the next four terms as follows:
- Fourth term: 7/8
- Fifth term: 9/8
- Sixth term: 11/8
- Seventh term: 13/8

Therefore, the next four terms for the sequence 1/4n are 7/8, 9/8, 11/8, 13/8.

3. Sequence: 23+n
- The first term is 23+1 = 24
- To find the second term, we add 1 again: 23+2 = 25
- To find the third term, we add 1 yet again: 23+3 = 26
- Continuing this pattern, we get the next four terms as follows:
- Fourth term: 27
- Fifth term: 28
- Sixth term: 29
- Seventh term: 30

Therefore, the next four terms for the sequence 23+n are 27, 28, 29, 30.

6. Divide each number by 4 to get the next number.

Ex: 160/4 = 40
What is 2.5/4?

8.
Add 3
Subtract (2 * 3)
Add (2 * 6)

Next: Subtract 2 * 12