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General

Easy

Question

# If a, b, c are in A.P then , are in

- A.P.
- G.P.
- H.P.
- A.G.P

Hint:

### If a, b , c are in AP. We know that in AP

**2 second term = first term + third term**

## The correct answer is: A.P.

### Given : a, b , c are in AP.

We know that in AP

2 second term = first term + third term

2b = a + c

Now,

(1) = =

Let

(2) Term2 () =

Term2 () =

Term2 () =

Term2 () =

Similarly,

(3) Term3 () =

Let , , be in AP

We can check if they satisfy the condition 2b = a + c

2 = +

Substituting the values

2 =

=

=

Taking m common and cancelling out from both sides

=

Thus, a, b, c are in A.P then , are in A.P.

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