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  • The 5th, 8th and 11th terms of a G.P. are p, q and s, respectively. Show that q raised to 2 equals ps.

3.  The 5 ^{th} , 8 ^{th} \: \:and \: \: 11 ^{th}  terms of a G.P. are p, q and s, respectively. Show  that q ^2 = ps

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To prove : q ^2 = ps

Let first term=a and common ratio = r

a_5=a.r^4=p..................(1)

a_8=a.r^7=q..................(2)

a_1_1=a.r^1^0=s..................(3)

Dividing equation 2 by 1, we have

\frac{a.r^7}{a.r^4}=\frac{q}{p}

\Rightarrow r^3=\frac{q}{p}

Dividing equation 3 by 2, we have

\frac{a.r^1^0}{a.r^7}=\frac{s}{q}

\Rightarrow r^3=\frac{s}{q}

Equating values of r^3 ,  we have

\frac{q}{p}=\frac{s}{q}

\Rightarrow q^2=ps

Hence proved

Posted by

seema garhwal

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