Answer:
81, 243, 729, 2187, 6561
Step-by-step explanation:
Note that the
third term 9 = 3²
fourth term 27 = 3³
Thus to obtain a particular term in the sequence we require the exponent to be one less than the terms position n in the sequence, that is
[tex]a_{n}[/tex] = [tex]3^{n-1}[/tex] , thus
first term 1 → [tex]3^{1-1}[/tex] = [tex]3^{0}[/tex] = 1
The next 5 terms in the sequence are
[tex]a_{5}[/tex] = [tex]3^{5-1}[/tex] = [tex]3^{4}[/tex] = 81
[tex]a_{6}[/tex] = [tex]3^{6-1}[/tex] = [tex]3^{5}[/tex] = 243
[tex]a_{7}[/tex] = [tex]3^{7-1}[/tex] = [tex]3^{6}[/tex] = 729
[tex]a_{8}[/tex] = [tex]3^{8-1}[/tex] = [tex]3^{7}[/tex] = 2187
[tex]a_{9}[/tex] = [tex]3^{9-1}[/tex] = [tex]3^{8}[/tex] = 6561
