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If 1/ a , 1/ b , 1/ c are in AP, prove that

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 (a + b + c )

If a constant is subtracted from each term of an A.P., the resulting sequence is also an A.P.
Substracting the above A.P. with 1