The sum of first three terms of a G.P. is 13/12 and their product is -1. Find the terms.

Question

The sum of first three terms of a G.P. is $\frac{13}{12}$ and their product is $- 1$ . Find the terms.

Smart Achievers · Accepted Answer

(1)

$Let \frac{a}{r}, a, a r be the first three terms of the G.P.$

$Then, \frac{a}{r} + a + a r = \frac{13}{12}$ ...(i)

$and (\frac{a}{r}) (a) (a r) = - 1 \Rightarrow a^{3} = - 1 \Rightarrow a = - 1$ ...(ii)

$Substituting a = - 1 in (i), we get$

$- \frac{1}{r} - 1 - r = \frac{13}{12} \Rightarrow 12 r^{2} + 25 r + 12 = 0 \Rightarrow r = \frac{- 3}{4}, \frac{- 4}{3}$

$But r = \frac{- 3}{4} is only possible value.$

$∴$ $The terms are \frac{4}{3}, - 1, \frac{3}{4}$

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