Question

In a GP, the 10th term is x and 12th term is y. Then the common ratio is
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Answer 1

Answer:

the ratio of the gp is 1 / r^2

Explanation:

let the gp be a,ar,ar^2............ar^9,a^10,ar^11......

=>a(10)=ar^9

=>a(12)=ar^11

=>a(10)/a(12)=1/r^2

Answer 2

HOPE IT HELPS :

Given :

$a_{10} = x$

$a_{12} = y$

Let the common ratio os the given GP be = r

Solution :

Let the 11th term of GP be  = $a_{11}$

As common ratio of a GP is constant for all the series

=>  $(a_{12} /a_{11}) = (a_{11} /a_{10})$

=> $a_{11} = \sqrt{a_{12} . a_{10}}$

=>$a_{11} = \sqrt{x.y}$

Hence common ratio of GP is :

r = $a_{11} / a_{12}$

r =$\sqrt{y/x}$

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