If a, b, c are in AP, show that 
are also in AP.
To prove: 
are in A.P.
Given: a, b, c are in A.P.
Proof: a, b, c
are in A.P.
If each term of an A.P. is multiplied by a constant, then the resulting sequence is also an A.P.
Multiplying the A.P. with (ab + bc + ac)
, are in A.P.
Multiplying the A.P. with 
, are in A.P.
, are in A.P.
If a constant is subtracted from each term of an A.P., the resulting sequence is also an A.P.
Substracting the A.P. with 1
, are in A.P.
, are in A.P.
On rearranging
, are in A.P.
Hence Proved
1