If frac{{x + y}}{2},;y,;frac{{y + z}}{2} are | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(b) If $\frac{{x + y}}{2},\;y,\;\frac{{y + z}}{2}$ are in $H.P.$, then

$y = \frac{{xy + xz + {y^2} + yz}}{{x + 2y + z}}$

$ \Rightarrow $ $xy + 2

Vedclass · Accepted Answer

$G.P.$

Vedclass · Answer

(b) If $\frac{{x + y}}{2},\;y,\;\frac{{y + z}}{2}$ are in $H.P.$, then

$y = \frac{{xy + xz + {y^2} + yz}}{{x + 2y + z}}$

$ \Rightarrow $ $xy + 2{y^2} + yz = xy + xz + {y^2} + yz$

$ \Rightarrow $${y^2} = xz$

Thus $x,\;y,\;z$ will be in $G.P.$

If $\frac{{x + y}}{2},\;y,\;\frac{{y + z}}{2}$ are in $H.P.$, then $x,\;y,\;z$ are in

Similar Questions

The first term of an infinite geometric progression is $x$ and its sum is $5$. Then

How many terms of the $G.P.$ $3, \frac{3}{2}, \frac{3}{4}, \ldots$ are needed to give the sum $\frac{3069}{512} ?$

If $a,\;b,\;c$ are ${p^{th}},\;{q^{th}}$ and ${r^{th}}$ terms of a $G.P.$, then ${\left( {\frac{c}{b}} \right)^p}{\left( {\frac{b}{a}} \right)^r}{\left( {\frac{a}{c}} \right)^q}$ is equal to

Find the sum of the sequence $7,77,777,7777, \ldots$ to $n$ terms.

If $x, {G_1},{G_2},\;y$ be the consecutive terms of a $G.P.$, then the value of ${G_1}\,{G_2}$ will be