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  • If the 4 th, 10 th and 16 th terms of a G.P. are x, y and z, respectively. Prove that x, y, z are in G.P.

17.  If the 4 ^{th} , 10 ^{th} , 16 ^ {th}  terms of a G.P. are x, y and z, respectively. Prove that x,y, z are in G.P.

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best_answer

Let x,y, z are in G.P.

Let first term=a and common ratio = r

a_4=a.r^3=x..................(1)

a_1_0=a.r^9=y..................(2)

a_1_6=a.r^1^5=z..................(3)

Dividing equation 2 by 1, we have

\frac{a.r^9}{a.r^3}=\frac{y}{x}

\Rightarrow r^4=\frac{y}{x}

Dividing equation 3 by 2, we have

\frac{a.r^1^5}{a.r^9}=\frac{z}{y}

\Rightarrow r^4=\frac{z}{y}

Equating values of r^4 ,  we have

\frac{y}{x}=\frac{z}{y}

Thus, x,y,z are in GP

Posted by

seema garhwal

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