SOLUTION: Please help me this question If A,B,C and X,Y,Z are are two arithmetic sequence,then A+x,B+y,C+Z is are arithmetic sequence

Question 1144811: Please help me this question

If A,B,C and X,Y,Z are are two arithmetic sequence,then A+x,B+y,C+Z is are arithmetic sequence
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

A,B,C is arithmetic meaning that
B = A+d
C = B+d = (A+d)+d = A+2d

In other words:
A,B,C
turns into
A,A+d,A+2d
for some real number d. Each new term is found by adding some number onto the prior term.

Through similar logic, we can turn
X,Y,Z
into
X,X+e,X+2e
where 'e' plays the same role as d above in the prior sequence.

Add the sequences by pairing up the corresponding values
A+X = A+X
B+Y = (A+d)+(X+e) = (A+X) + (d+e)
C+Z = (A+2d)+(X+2e) = (A+X) + (2d+2e) = (A+X)+2(d+e)

As you can see, the sequence
A+X, (A+X) + (d+e), (A+X)+2(d+e)
is in the form A+n*d which is of arithmetic form

Therefore, the original claim is true.

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