arrange the following from least to greatest common difference. (least on the bottom and highest on top) (1 point)
1049, 1052, 1055, 1058...
y=2x+4
an= -3+(n-1)10
-15,-4,7,18...
To arrange the given sequences from least to greatest common difference, let's analyze each sequence separately:
Sequence 1: 1049, 1052, 1055, 1058...
In this sequence, the common difference is 3, because each term is 3 greater than the previous one. So, the sequence can be written as:
1049, 1052, 1055, 1058...
Sequence 2: y = 2x + 4
This is an arithmetic sequence in equation form. To find the common difference, we can rewrite the equation in the form y = mx + c, where m represents the common difference. Comparing the equation to this form, we can see that the common difference is 2.
Sequence 3: an = -3 + (n-1)10
Here, an represents the nth term of the sequence. To find the common difference, we need to subtract an from the next term an+1. So, let's calculate that:
an+1 = -3 + (n+1-1)10
= -3 + n*10
Therefore, the common difference is 10.
Sequence 4: -15, -4, 7, 18...
In this sequence, the common difference is 11, because each term is 11 greater than the previous one. So, the sequence can be written as:
-15, -4, 7, 18...
Now, let's arrange these sequences from least to greatest common difference:
-15, -4, 7, 18... (common difference: 11)
1049, 1052, 1055, 1058... (common difference: 3)
y = 2x + 4 (common difference: 2)
an = -3 + (n-1)10 (common difference: 10)
Therefore, the arranged sequences from least to greatest common difference are:
-15, -4, 7, 18...
1049, 1052, 1055, 1058...
y = 2x + 4
an = -3 + (n-1)10
-15, -4, 7, 18...
1049, 1052, 1055, 1058...
From least to greatest common difference:
-15, -4, 7, 18...
1049, 1052, 1055, 1058...
To arrange the given sequences from least to greatest common difference, we need to calculate the common difference for each sequence.
1) Sequence:
1049, 1052, 1055, 1058...
To find the common difference, we subtract any number from its previous number. Let's calculate the differences:
1052 - 1049 = 3 (common difference)
1055 - 1052 = 3 (common difference)
1058 - 1055 = 3 (common difference)
Since the common difference remains the same (3), the sequence has a constant common difference.
Therefore, the arrangement from least to greatest common difference is:
1049, 1052, 1055, 1058...
2) Sequence:
-15, -4, 7, 18...
To find the common difference, we subtract any number from its previous number. Let's calculate the differences:
-4 - (-15) = 11 (common difference)
7 - (-4) = 11 (common difference)
18 - 7 = 11 (common difference)
Since the common difference remains the same (11), the sequence has a constant common difference.
Therefore, the arrangement from least to greatest common difference is:
-15, -4, 7, 18...
Lastly, the given equation y = 2x + 4 and the term formula an = -3 + (n - 1)10 do not involve sequences or common differences, so they cannot be arranged in that sense.