1.Write a rule for the sequence
-5,-4,-13,-22
2. Find the next three terms of the sequence
-4.-8.-16.-32
3.What is the 9th term in the following sequence
11,17,23,29
1. Rule: Subtract 1 from the previous term, then multiply by 3, then subtract 2. So, starting with -5, the sequence would be: -5, (-5 - 1) * 3 - 2 = -4, (-4 - 1) * 3 - 2 = -13, (-13 - 1) * 3 - 2 = -22.
2. Next three terms: To find the next term, divide the previous term by 2. So, starting with -32, the next three terms would be: -32 / 2 = -16, -16 / 2 = -8, -8 / 2 = -4.
3. The 9th term: To find the 9th term, add 6 to each term. So, starting with 11, the 9th term would be: 11 + (6 * 8) = 59. Because math makes me do it, I guess I should mention that you could also write the rule as add 6 to the (n-1)th term, where n is the position of the term you want to find. But where's the fun in that?
1. In the given sequence -5, -4, -13, -22, we can observe that each term is obtained by subtracting the previous term by 9. Therefore, the rule for the sequence is to subtract 9 from the previous term to obtain the next term.
2. To find the next three terms of the sequence -4, -8, -16, -32, we can observe that each term is obtained by multiplying the previous term by -2. Therefore, the next three terms would be -64, 128, -256.
3. In the sequence 11, 17, 23, 29, we can observe that each term is obtained by adding 6 to the previous term. Therefore, to find the 9th term, we can start with the first term of 11 and add 6 repeatedly. 11, 17, 23, 29, 35, 41, 47, 53, 59. Therefore, the 9th term in the sequence is 59.
To write a rule for a sequence, we need to identify the pattern or relationship between each term.
1. For the sequence -5, -4, -13, -22, let's analyze the differences between consecutive terms:
-4 - (-5) = 1
-13 - (-4) = -9
-22 - (-13) = -9
We can observe that the differences between consecutive terms are alternating between 1 and -9. Therefore, we can write the rule for this sequence as follows:
- Start with -5
- Add 1 to the previous term for the next term, then subtract 9 for the subsequent term.
2. To find the next three terms of the sequence -4, -8, -16, -32, we can analyze the pattern:
-8 - (-4) = -4
-16 - (-8) = -8
-32 - (-16) = -16
We can observe that the differences between consecutive terms are the same as the previous term multiplied by 2. Therefore, we can write the rule for this sequence as follows:
- Start with -4
- Multiply the previous term by 2 for the next term.
Using this rule, we can find the next three terms:
-32 x 2 = -64
-64 x 2 = -128
-128 x 2 = -256
So, the next three terms are: -64, -128, -256.
3. To find the 9th term in the sequence 11, 17, 23, 29, we can observe that each term increases by 6.
Therefore, we can write the rule for this sequence as follows:
- Start with 11
- Add 6 to the previous term for the next term.
Using this rule, we can find the 9th term:
11 + (6 x 8) = 11 + 48 = 59
So, the 9th term in the sequence is 59.
What do you notice about the patterns? What do you think?
Since you are studying this topic, you must have
the formulas and methods for this.
State your answers and we will correct them if necessary.
btw, I found no discernable pattern for #1.
#1. I think you meant 5,-4,-13,-22. If so, there is a common difference of -9 between terms.
#2 is powers of 2
#3 adds 6