SOLUTION: The xth, yth, and zth terms of a sequence are X,Y,Z respectively. Show that if the sequence is arithmetic then X(y-z) + Y(z-x) + Z(x-y)=0.

Question 1110008: The xth, yth, and zth terms of a sequence are X,Y,Z respectively. Show that if the sequence is arithmetic then X(y-z) + Y(z-x) + Z(x-y)=0.

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Let it be that in an arithmetic sequence
= first term of the arithmetic sequence
= common difference of the arithmetic sequence.
Then, if the xth, yth, and zth terms of athat sequence are X,Y,Z respectively,
,
, and
.

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