Question

FOR A G.P SUM OF FIRST 3 TERMS IS 125 AND SUM OF NEXT THREE TERMS IS 27 FIND THE VALUE OF r​

Answer 1

Given,

Sum of first three terms of G.P. $\[ = 125\]$

Sum of next three terms of G.P. $\[ = 27\]$

Solution,

Consider the G.P. is $\[a,ar,a{r^2},a{r^3},a{r^4},a{r^5},a{r^6}, - - - \]$

$\[a + ar + a{r^2} = 125\]$-------(1)

$\[\begin{array}{l}a{r^3} + a{r^4} + a{r^5} = 27\\{r^3}\left( {a + ar + a{r^2}} \right) = 27\end{array}\]$--------(2)

Put value of equation 1 in equation 2,

$\[\begin{array}{l}{r^3}\left( {a + ar + a{r^2}} \right) = 27\\ \Rightarrow {r^3} \times 125 = 27\\ \Rightarrow {r^3} = \frac{{27}}{{125}}\\ \Rightarrow r = \frac{3}{5}\end{array}\]$

Hence the common ratio (r) of G.P. is $\[\frac{3}{5}\]$.