If general term of a G.P. with common ratio ${}^{\text{'}}r^{\text{'}}$ be $t_{k+1}$ and general term of another G.P. with common ratio ${}^{\text{'}}r^{\text{'}}$ be $t_{k+1}^{\text{'}}$, then the series whose general term $t_{k+1}^{\text{'}\text{'}}=t_{k+1}+t_{k+1}^{\text{'}}$ is

$\mathrm{I}.$ An A.P. with common difference ${}^{\text{'}}r^{\text{'}}$

$\mathrm{II}.$ A G.P. with common ratio ${}^{\text{'}}r^{\text{'}}$

$\mathrm{III}.$ A H.P.

Which of the above statement(s) is/are correct?