Statement 1 : 1,2,4,8,.. is a G.P., 4,8,16,32 is a G.P. and $1+4,2+8,4+16,8+32,\mathrm{.......}$  is also a G.P.
Statement 2 : Let general term of a G.P. with common ratio r be  ${\text{T}}_{k+1}$ and general term of another G.P. with common ratio r be $T{\text{'}}_{k+1}$  then the series whose general term $T\text{'}{\text{'}}_{k+1}=T_{k+1}+T{\text{'}}_{k+1}$ is also a G.P. with common ratio r.