The numbers
38, x, -8, and y
form an arithmetic sequence. Compute
x+y
I can find x-y but not x+y
x-38 = -8-x
so
2 x = 30
x = 15
-8-x = y -(-8) = y+8
-8 - 15 = y + 8
-23 = y + 8
y = -31
x+y = 15-31 = -16
To find the sum of two numbers in an arithmetic sequence, we need to determine the common difference between the numbers in the sequence.
In this case, the arithmetic sequence is formed by the numbers 38, x, -8, and y.
To find the common difference, we subtract each pair of consecutive terms.
The difference between x and 38 is x - 38.
The difference between -8 and x is x - (-8), which simplifies to x + 8.
The difference between y and -8 is y - (-8), which simplifies to y + 8.
Since it is an arithmetic sequence, the common difference should be the same for all the differences we found above. So we can set up two equations based on the differences as follows:
x - 38 = x + 8,
y + 8 = x + 8.
Simplifying the first equation, we get:
x - x = 8 + 38,
0 = 46.
This equation is inconsistent and has no solution. Therefore, there is no value for x that would satisfy the conditions given in the problem.
Without a specific value for x, we cannot compute x + y.