Use the image to answer the question.

A four-quadrant coordinate plane includes three unlabeled points in quadrant 1. They are arranged in a generally linear downward trend. The x- axis labeled n. The y-axis is labeled f left parenthesis n right parenthesis. The x-axis ranges from negative 9 to 9 increments of 1. The y-axis ranges from negative 11 to 11 in increments of 1. The points are plotted at left parenthesis 1 comma 9 right parenthesis, left parenthesis 2 comma 5 right parenthesis, and left parenthesis 3 comma 1 right parenthesis.

The graph represents an arithmetic sequence. Find the common difference, d , the fourth term, a4 , and the fifth term, a5 , of the arithmetic sequence.

(2 points)
d=

a4=

a5=

7 answers

To find the common difference, we can look at how the y-values change as the x-values increase by 1. From (1, 9) to (2, 5), the y-values decrease by 4. This means that the common difference, d , is -4.

The fourth term, a4 , can be found by adding the common difference twice to the last known term (3, 1):
a4 = 1 + (-4) + (-4) = -7

Similarly, the fifth term, a5 , can be found by adding the common difference three times to the last known term (3, 1):
a5 = 1 + (-4) + (-4) + (-4) = -11

So,
d = -4
a4 = -7
a5 = -11
-7 and -11 are wrong
My apologies for the errors. Let's re-calculate:

The common difference, d , can be found by subtracting the y-values of two consecutive points. For example, (2, 5) and (1, 9) have a common difference of -4.

Therefore, d = -4.

To find the fourth term, a4 , we can use the common difference. Starting from the third term (3, 1), we can subtract the common difference twice to get:
a4 = 1 - (-4) - (-4) = 1 + 4 + 4 = 9

To find the fifth term, a5 , we can again use the common difference. Starting from the third term (3, 1), we can subtract the common difference three times to get:
a5 = 1 - 3(-4) = 1 + 12 = 13

Therefore,
d = -4,
a4 = 9,
a5 = 13.
9 and 13 are also wrong
Apologies for the mistakes. Let's recalculate:

Common difference, d: From the points (1, 9) and (2, 5), the y-values decrease by 4. So, d = -4.

To find the fourth term, a4:
Starting from the third term (3, 1), we can subtract the common difference twice:
a4 = 1 + (-4) + (-4) = 1 - 4 - 4 = -7

To find the fifth term, a5:
Starting from the third term (3, 1), we can subtract the common difference three times:
a5 = 1 + (-4) + (-4) + (-4) = 1 - 4 - 4 - 4 = -11

Therefore,
d = -4,
a4 = -7,
a5 = -11.
9 , 13 , -7, and -11 are wrong
Apologies for the errors in the previous responses. Let's calculate them correctly this time.

Common difference, d: From the points (1, 9) and (2, 5), the y-values decrease by 4. So, d = -4.

To find the fourth term, a4:
Starting from the second term (2, 5), we need to subtract the common difference twice:
a4 = 5 + (-4) + (-4) = 5 - 4 - 4 = -3

To find the fifth term, a5:
Starting from the second term (2, 5), we need to subtract the common difference three times:
a5 = 5 + (-4) + (-4) + (-4) = 5 - 4 - 4 - 4 = -7

Therefore,
d = -4,
a4 = -3,
a5 = -7.