Step 1: Write out the nth term of a geometric sequence
[tex]\begin{gathered} a_n=a_1r^{n-1} \\ a_1=\text{first term} \\ r=\text{common ratio} \end{gathered}[/tex]
Step 2: Write out the sequence and calculate for a1 and r
[tex]\begin{gathered} 1024,512,256,\ldots \\ a_1=1024 \\ r=\frac{a_2}{a_1}=\frac{512}{1024}=\frac{1}{2} \end{gathered}[/tex]
Step 3: Write out the formula for the sixth term and substitute a1 and r
[tex]\begin{gathered} a_6=a_1r^{6-1} \\ =a_1r^5 \end{gathered}[/tex][tex]\begin{gathered} a_6=1024(\frac{1}{2})^5 \\ =1024(\frac{1}{32}) \\ a_6=32 \end{gathered}[/tex]
Hence the sixth term is 32
