Question

How many terms of the $G.P.3,\frac{3}{2},\frac{3}{4}.......$ are needed to give the sum $\frac{3069}{512}$?.

Answer 1

$a=3$

$r=\frac{1}{2}$

sum of n terms in a GP =

$\frac{a(1-r^n)}{(1-r)}$

then ,

$\frac{3069}{512}=\frac{3(1-{\left(\frac{1}{2}\right)}^n)}{(1-\frac{1}{2})}$

now , after solving is we get

value of $n=10$