Q. 185.0( 1 Vote )

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

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

Here, first term = a

Common difference, d1 = b – a … (1)

and d2 = c – b … (2)

Consider, and,

Common difference, d3 = -

=

= … (3)

d4 = -

=

= … (4)

From (1) and (2),

d1 = d2

b – a = c – b

Dividing both sides by abc,

=

d3 = d4 [From (3) and (4)]

Hence,, and are in A.P.

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