Question

in a GP the 4th term is 24 and the 7 term is 192.find the sum of 1st 10 terms

Answer 1

$4th \: ter m \: = \: xy {}^{3}$
$7th \: term = xy {}^{6}$
then
$y {}^{3} = 8$
then, y = 2, and therefore x =3
now the series is 3,6,12,24,48,96,192,384,768,1536
then the sum is 3069.
Or you can use the summation formula instead.