# Let be a polynomial function of second degree. If and are in A.P., then  are in  Option 1) G.P. Option 2) H.P. Option 3) Arithmetic­Geometric Progression Option 4) A.P.

Answers (1)

As we learnt in

Properties of an A.P. -

If each term of an AP is multiplied by a fixed constant (or divided by a constant),then resultant is also an AP.

- wherein

If

Then

and

Let the polynomial be

Now, a, b, c in AP

So 2Aa, 2Ab, 2Ac in AP

So  in AP

Option 1)

G.P.

This option is incorrect.

Option 2)

H.P.

This option is incorrect.

Option 3)

Arithmetic­Geometric Progression

This option is incorrect.

Option 4)

A.P.

This option is correct.

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