Question
If are in A.P., prove that are in A.P.
Solution
Since are in A.P.
∴
or
or (b - a) (2c - a - b) = (c - b) (2a - b - c) ...(i)
Now, will be in A.P.
if or if =
or if (Note this step carefully)
or if (b - a) (2c - a - b) = (c - b) (2a - b - c) which is true. [By using (i)]
Hence, are in A.P.