Question

if x,2y,3z are in AP, where the distinct numbers x,y,z are in GP,then the common ratio of the GP is??​

Answer 1

Question -:

if x,2y,3z are in AP, where the distinct numbers x,y,z are in GP,then the common ratio of the GP is??

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SOLUTION -:

Given -:

• ➣ if x,2y,3z are in AP,
• ➣ x,y,z are in GP,

To Find

• ➣ common ratio of GP

Required Answer

➣ r = 1/3

Since x , 2y ,3z are in AP

$\displaystyle \because 4y = x + 3z$

and x and y and z are in GP

y = rx and z = xr²

on putting the value of y and z in equation i

we get,,

$\displaystyle \:4xr = x \: + {3xr}^{2}$

$\displaystyle \implies \: {3r}^{2} - 4r \: + 1 = 0$

$\displaystyle \implies \: (3r - 1) \: (r - 1) = 0$

$\displaystyle \: r = \frac{1}{3} \: \: or \: 1$

$\displaystyle\bold{r \: = \frac{1}{3} }$