If are in AP, prove that

(i) are in AP.


(ii) are in AP.


(i) are in A.P.


To prove: are in A.P.


Given: are in A.P.


Proof: 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 ( a + b + c )


are also 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 above A.P. with 1


, are also in A.P.


, are also in A.P.


, are also in A.P.


Hence Proved


(ii) are in A.P.


To prove: are in A.P.


Given: are in A.P.


Proof: 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 ( a + b + c )


are also 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 above A.P. with 2


, are also in A.P.


, are also in A.P.


, are also in A.P.


Hence Proved


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