Q. 185.0( 1 Vote )

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

Answer :

Given, a, b, c are in A.P.

Here, first term = a

Common difference, d_{1} = b – a … (1)

and d_{2} = c – b … (2)

Consider, and,

Common difference, d_{3} = -

=

= … (3)

⇒ d_{4} = -

=

= … (4)

From (1) and (2),

⇒ d_{1} = d_{2}

⇒ b – a = c – b

Dividing both sides by abc,

⇒ =

⇒ d_{3} = d_{4} [From (3) and (4)]

Hence,, and are in A.P.

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