The common ratio between terms is 3, so the sequence has general [tex]n[/tex]-th term
[tex]a_n=3^{n-1}[/tex]
for [tex]n\ge1[/tex]. The term exceeds 7000 when
[tex]3^{n-1}>7000\implies n-1>\log_37000\implies n>1+\log_37000\approx9.06[/tex]
which means the first time [tex]a_n[/tex] exceeds 7000 occurs when [tex]n=10[/tex]. Indeed,
[tex]a_{10}=3^{10-1}=19,683[/tex]
while the previous term would have been
[tex]a_9=3^{9-1}=6561[/tex]
