Answer :

To prove: a2(b + c), b2(c + a), c2(a + b) are in A.P.

Given: are in A.P.

Proof:are in A.P.

are in A.P.

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 (abc)

, are in A.P.

are in A.P.

[(a2c + a2b)], [ab2 + b2c], [c2b + ac2] are in A.P.

On rearranging,

[a2(b + c)], [b2(c + a)] , [c2(a + b)] are in A.P.

Hence Proved

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