Geometric progression

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If the product of three terms of a G.P is 216 and the sum of their products taken in pairs is 156 then the greatest term is

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$Let the terms are (\frac{a}{r}), (a), (ar)$
$\begin{array}{l} Given that (\frac{a}{r}) (a) (a r) = 216 \\ \to a = 6 \\ g i v e n t h a t (\frac{a}{r} \cdot a) + (\underset{}{\underset{}{a}) (a r)} + (ar \cdot a / r) = 156 \end{array}$
$\begin{aligned} \to a^{2} (\frac{1}{r} + r + 1) = 156 \sin c e a = 6 \\ \Rightarrow 3 r^{2} - 10 r + 3 = 0 \to r = 3 o r 1 / 3 \end{aligned} \begin{array}{l} ∴ the terms are 2, 6, 18 \\ ∴ the greatest term is 18 \end{array}$

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Geometric progression

Remember concepts with our Masterclasses.

If the product of three terms of a G.P is 216 and the sum of their products taken in pairs is 156 then the greatest term is

Let the terms are ar,(a),(ar) Given that ar( a )(ar)=216→a=6 given that ar⋅a+(a )(ar) +(ar⋅a/r)=156 →a21r+r+1=156 since a=6⇒3r2−10r+3=0→r=3 or 1/3 ∴ the terms are 2,6,18∴ the greatest term is 18

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