The graph represents an arithmetic sequence. Find the common difference, d , the fourth term, a4 , and the fifth term, a5 , of the arithmetic sequence.
point A : (1,9)
point B :(2,5)
point C:(3,1)
(2 points)
d=
a4=
a5=
To find the common difference, we can use points A and B.
Using the formula for the common difference in an arithmetic sequence:
d = (y2 - y1) / (x2 - x1)
d = (5 - 9) / (2 - 1)
d = -4
So, the common difference is -4.
To find a4, we start with the first term (a1) and add the common difference three times.
a4 = a1 + 3d = 9 + 3(-4) = 9 - 12 = -3
Therefore, the fourth term (a4) is -3.
To find a5, we start with the first term (a1) and add the common difference four times.
a5 = a1 + 4d = 9 + 4(-4) = 9 - 16 = -7
Therefore, the fifth term (a5) is -7.