Question 1143271: Given the arithmetic sequence x,y,30,z,f. Find x+y+z+f?
A)60
B)80
C)120
D)130
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website!
Let the common difference be d. Then these equations are true,
so add all the left sides and all the right sides:
y = 30-d
x = 30-2d
z = 30+d
f = 30+2d
-------------------------
y+x+z+f = 120
Notice that there are lots of different possibilities for x,y,z,f.
For example the arithmetic sequence could be
10 20 30 40 50, which have sum 120 with d=10, or
20 25 30 35 40, which also have sum 120 with d=5, or
54 42 30 18 6, which also have sum 120 with d=-12, or any of
an infinite number of possible arithmetic sequences. But the
sum will always be 120. That's interesting!
Edwin
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