Given the sequence: 5,15,45,135
In general, the sequence for the n-th term is given by:
[tex]a_n=a_1\cdot r^{n-1}[/tex]Where:
r = common ratio
a1 = first term
Therefore:
[tex]\begin{gathered} a_1=5 \\ r=\frac{15}{5}=3 \end{gathered}[/tex]And we find a6:
Substitute a1 and r in the formula
[tex]a_6=5\cdot3^{6-1}=5\cdot3^5=5\cdot243=1215[/tex]Answer: a6 = 1215
