Answer:
the explicit formula for given geometric sequence {1,-3,9,..} is [tex]a_{n}= (-3)^{n-1}[/tex]
Step-by-step explanation:
We are given the series
1,-3,9,...
the common ratio is:
-3/1 = -3
9/-3 = -3
So, the common ratio in the series is -3
a₁ = 1
The formula used for geometric series is:
[tex]a_{n}= a_{1}(r)^{n-1}[/tex]
Putting values of a₁ and r
[tex]a_{n}= 1(-3)^{n-1}[/tex]
[tex]a_{n}= (-3)^{n-1}[/tex]
So, the explicit formula for given geometric sequence {1,-3,9,..} is [tex]a_{n}= (-3)^{n-1}[/tex]
