If $a, b, c$ are in A.P, then $a / b c, 1 / c, 1 / b$ are in

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Solution

Finding the progression of the terms $a / b c, 1 / c, 1 / b$ :
Given $a, b, c$ are in $A . P$
So $c - b = b - a;$ ……….(i)
$(1 / b) - (1 / c) = (c - b) / b c . . . (i i)$
Since $(c - b) = (b - a)$
From $(i) a n d (i i)$
we get $(1 / b) - (1 / c) = (1 / c) - (a / b c)$
So $a / b c, 1 / c, 1 / b$ are in $A . P$
Hence, the terms $a / b c, 1 / c, 1 / b$ are in AP

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