The variables that we have in a geometric progression are
a , which is the first term = [tex] \frac{7}{9} [/tex]
r which is the common ratio got by dividing any two consecutive terms
[tex] r= \frac{\frac{-7}{3}}{\frac{7}{9}} [/tex]
[tex] r= \frac{-7}{3} . \frac{9}{7} [/tex]
[tex] r=-3 [/tex]
n is the number of terms = 9
The n th term is given by the formula
a₉ = a.[tex] r^{n-1} [/tex]
[tex] =\frac{7}{9}. (-3)^{9-1} [/tex]
[tex] \frac{7}{9} .(-3)^{8} [/tex]
=[tex] \frac{7}{9} . 6561 [/tex]
=[tex] \frac{45927}{9} [/tex]
a₉ = 5103
