Question

in a gp,2nd term is 24,5th term is 1280.find common ratio​

Answer 1

Answer:

$r=4(\sqrt[3]{\frac{5}{6} })$

Step-by-step explanation:

given:

2nd term = 24

5th term = 1280

general form 'n' th term  of a GP is --   $T_{n} = ar^{n-1}$  

where  a  =   first term of gp

           r = common ratio of gp

we have,

$T_{2} = 24$                                  |        $T_{5} = 1280$

$ar^{2-1} = 24$                             |       $ar^{5-1} = 1280$

$ar = 24$   --------------( 1 )          |       $ar^{4} = 1280$ ---------------- ( 2 )

now divide equation 2 by 1.

$\frac{ar^{4}}{ar} = \frac{1280}{24}$

$r^{3} = \frac{1280}{24}$

$r=\sqrt[3]{\frac{64*20}{24} }$

hence the common ratio is ....

$r=4(\sqrt[3]{\frac{5}{6} })$      (  simply r = 3.764 )

thus you got the answer.                  

Hope it  helps !