The nth term of a geometric sequence is expressed as:
[tex]a_n=ar^{n-1}[/tex]were:
• a is the first term
,• r is the common ratio
,• n is the number of terms
If the 2nd term a₂ = 28, then;
[tex]\begin{gathered} 28=ar^{2-1} \\ ar=28 \end{gathered}[/tex]If the 5th term a₅ = 1792, then;
[tex]\begin{gathered} 1792=ar^{5-1} \\ ar^4=1792 \end{gathered}[/tex]Take the ratio of both equations to have:
[tex]\begin{gathered} \frac{ar^4}{ar}=\frac{1792}{28} \\ r^3=64 \\ r=\sqrt[3]{64} \\ r=4 \end{gathered}[/tex]Substitute r = 4 into any of the equations to have:
[tex]\begin{gathered} ar=28 \\ 4a=28 \\ a=\frac{28}{4} \\ a=7 \end{gathered}[/tex]Determine the rule for the nth term of the geometric sequence. Recall that;
[tex]\begin{gathered} a_n=ar^{n-1} \\ a_n=7(4)^{n-1} \end{gathered}[/tex]This gives the nth term of the geometric sequence