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Insert two number between 3 an 81 so that the resulting sequence is G.P.
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Verified Answer
Let $G_1, G_2$ be the two numbers such that
$3, G_1, G_2, 81$ are in G.P.
Let $r$ be the common ratio,
$T_4=a r^{n-1}=81$ or $3 \cdot r^3=81$
$\therefore \quad r^3=\frac{81}{3}=27=3^3 \quad \therefore r=3$ $\mathrm{G}_1=a r=3 \times 3=9 ; \mathrm{G}_2=a r^2=3 \times 3^2=27$
9,27 are the required number
$3, G_1, G_2, 81$ are in G.P.
Let $r$ be the common ratio,
$T_4=a r^{n-1}=81$ or $3 \cdot r^3=81$
$\therefore \quad r^3=\frac{81}{3}=27=3^3 \quad \therefore r=3$ $\mathrm{G}_1=a r=3 \times 3=9 ; \mathrm{G}_2=a r^2=3 \times 3^2=27$
9,27 are the required number
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