Given conditions:
6th term (T6) = -2
first term (a) = 18
n = 6, r = ?
Formula for finding the nth term of a GP:
[tex]tn = a {r}^{n - 1} [/tex]
Where:
T = the given value for the number of term(s)
n = the given number of term
a = The first term
r = The common ratio
Replacing for the values:
[tex] - 2 = 18 {r}^{6 - 1} \\ - 2 = 18 {r}^{5} [/tex]
Dividing both sides by 18, we have:
[tex] {r}^{5} = \frac{ - 2}{18} [/tex]
Now, we have to fifth root both sides to find the value of r.
[tex] \sqrt[5]{ {r}^{5} } = \sqrt[5]{ \frac{ - 2}{18} } [/tex]
Therefore:
Common ratio, [tex]r = -0.0638165752[/tex] [tex]≈ -0.064[/tex] to 3 decimal places.
