We have the sequence:
[tex]\begin{gathered} a_1=7, \\ a_2=14, \\ a_3=28, \\ a_4=56, \\ \ldots \end{gathered}[/tex]We rewrite the sequence as:
[tex]\begin{gathered} a_1=7\cdot1=7\cdot2^0=7\cdot2^{1-1}, \\ a_2=7\cdot2=7\cdot2^1=7\cdot2^{2-1}, \\ a_3=7\cdot4=7\cdot2^2=7\cdot2^{3-1}, \\ a_4=7\cdot8=7\cdot2^3=7\cdot2^{4-1}, \\ \ldots \end{gathered}[/tex]From the previous equations, we see that the general term is given by:
[tex]a_n=7\cdot2^{n-1}.[/tex]Replacing n = 19, we get:
[tex]a_{19}=7\cdot2^{19-1}=7\cdot2^{18}=7\cdot262144=1835008.[/tex]Answer
[tex]a_{19}=7\cdot2^{18}=1835008[/tex]