Question

Which term of the G.P. $4,-8,16,-\mathrm{32......}$ is $1024$?

Answer 1

Let the $n$ th term of the G.P. $4,-8,16,-\mathrm{32......}$ is $1024$.

$a=4$ and $r=\frac{-8}{4}=-2$

Then we've,

$a\times (r{)}^{n-1}=a_n$

$4\times (-2{)}^{n-1}=1024$ [ Since the first term of the G.P. is $4$ and the common ratio is $-2$]

$(-2{)}^{n-1}=256$

$(-2{)}^{n-1}=(-2{)}^8$

$n-1=8$

$n=9$.