Step 1: Write out the terms in the question
[tex]\begin{gathered} a_6=48 \\ a_7=96 \\ a_8=192 \\ a_9=384 \end{gathered}[/tex]Step 2: Find the common ratio ( r )
The ratio between two consecutive terms gives the common ratio
That is,
[tex]r=\frac{a_7}{a_6}=\frac{a_8}{a_7}=\frac{a_9}{a_8}[/tex][tex]r=\frac{96}{48}=2[/tex]Step 3: Find the first term by substituting the value of r
Firstly, write out the general term of a geometric progression
[tex]\begin{gathered} a_n=a_1\text{ }\times r^{n-1} \\ \text{Thus,} \\ a_6=a_1r^5=48 \\ a_{1\text{ }}\text{ is the first term} \end{gathered}[/tex][tex]\begin{gathered} \text{IF a}_1\times r^5=48 \\ a_1\times2^5=48 \\ a_1\times32=48 \\ a_1=\frac{48}{32}=\frac{3}{2} \end{gathered}[/tex]Thus, the first term is 3/2
