Question

What is the 9th term of the geometric sequence 7/9, -7/3, 7, -21, 63

Answer 1

When we look at the sequence, we can see that the change is *-3 each time. So we simply do that until the 9th term
7/9, -7/3, 7, -21, 63, -189, 567, -1701, 5103

Hope this helps

Answer 2

The variables that we have in a geometric progression are

a , which is the first term =
`(7)/(9)`

r which is the common ratio got by dividing any two consecutive terms

`r= ((-7)/(3))/((7)/(9))`

`r= (-7)/(3) . (9)/(7)`

`r=-3`

n is the number of terms = 9

The n th term is given by the formula

a₉ = a.
`r^(n-1)`

`=(7)/(9). (-3)^(9-1)`

`(7)/(9) .(-3)^(8)`

=
`(7)/(9) . 6561`

=
`(45927)/(9)`

a₉ = 5103