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Summation by Sigma Method

If x≠ y and...

Question

If $x \neq y$ and the sequences $x, a_{1}, a_{2}, y$ and $x, b_{1}, b_{2}, y$ each are in $A . P$ ., then $(\frac{a_{2} - a_{1}}{b_{2} - b_{1}})$

\frac{2}{3}

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\frac{3}{2}

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1

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\frac{3}{4}

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Solution

The correct option is C $1$
Given $x \neq y$
$x, a_{1}, a_{2}, y    a r e i n A P x, b_{1}, b_{2}, y \to c d = \frac{y - x}{n + 1}$
$c d$ (common difference) $= \frac{y - x}{n + 1}$
We have to find $\frac{a_{2} - a_{1}}{b_{2} - b_{1}}$
$= \frac{c d}{c d}$
$= 1$

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