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Home  >>  CBSE XI  >>  Math  >>  Sequences and Series
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The sum of first $3$ terms of a G.P is $\large\frac{39}{10}$ and their product is $1$. Find the common ratio and the terms of the G.P.

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  • Assume any three terms of a G.P as $\large\frac{a}{r},$$a,ar$
  • Sum of $n$ terms of a G.P.=$S_n=a.\large\frac{r^n-1}{r-1}$
Let the three terms of the G.P. be $\large\frac{a}{r},$$a,ar$
Given that sum of the three terms$=\large\frac{39}{10}$
Also given that their product $=1$
$\Rightarrow\:\large\frac{a}{r}$$\times a \times ar=1$
$\Rightarrow\:a^3=1$ or $a=1$
Substituting the value of $a$ in (i) we get
Solving this quadratic equation we get
Substituting the value of $a\:\:and\:\:r$ the three numbers are
answered Feb 26, 2014 by rvidyagovindarajan_1

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