The geometric sequence is given by:
[tex]\begin{gathered} a_n=ar^{n-1} \\ where\colon \\ a=first_{\text{ }}term_{\text{ }}of_{\text{ }}the_{\text{ }}sequence \\ r=common_{\text{ }}ratio \end{gathered}[/tex]so:
[tex]\begin{gathered} a_1=6 \\ r=2 \\ a_1=a\cdot2^{1-1}=a\cdot2^0=a=6 \\ so\colon \\ a=6 \end{gathered}[/tex]Therefore, the geometric sequence is:
[tex]\begin{gathered} a_n=6\cdot2^{n-1} \\ \end{gathered}[/tex]the sum of the first five terms of a geometric series will be:
[tex]\sum ^5_{n\mathop=1}6\cdot2^{n-1}=6+12+24+48+96=186[/tex]For n = 5
[tex]a_5=6\cdot2^{5-1}=6\cdot2^4=6\cdot16=96[/tex]