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Question
If a, b, c are three consecutive terms of an A.P. and x, y, z are three consecutive terms of a G.P. Then prove that xb – c. yc – a . za – b = 1
Solution
We have a, b, c as three consecutive terms of A.P.
Then b – a = c – b = d ...(say)
c – a = 2d
a – b = – d
Now xb – c . yc – a . za – b = x–d . y2d . z–d
= `x^(-d) (sqrt(xz))^(2d) * z^(-d)` ....`("Since" y = (sqrt(xz))) "as" x, y, z "are" "G.P.")`
= `x^(-d) * x^d * z^d * z^(-d)`
= `x^(-d + d) * z^(d - d)`
= `x^o z^o` = 1
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