Respuesta :
Answer:
Step-by-step explanation:
A geometric sequence is a sequence in which the successive terms increase or decrease by a common ratio. The formula for the nth term of a geometric sequence is expressed as follows
Tn = ar^(n - 1)
Where
Tn represents the value of the nth term of the sequence
a represents the first term of the sequence.
n represents the number of terms.
From the information given,
r = 1/3
T3 = - 81
n = 3
Therefore,
- 81 = a× 1/3^(3 - 1)
-81 = a × (1/3)^2
-81 = a/9
a = -81 × 9 = - 729
The exponential equation for this sequence is written as
Tn = - 729 * (1/3)^(n-1)
Answer:
[tex]t(n)=-729(\frac{1}{3}) ^{n-1}[/tex]
Step-by-step explanation:
Given:
A geometric sequence with third term = -81
Common ratio = [tex]\frac{1}{3}[/tex]
General term of a geometric sequence is given by the formula:
[tex]t(n)=ar^{n-1}[/tex]
where :
t(n) is nth term
a is the first term
r is the common ratio
n=1,2,3,4...
Here r=1/3 and t(3)=-81
[tex]ar^{2}=-81\\a\times\frac{1}{3}^{2}=-81\\a=-729[/tex]
General equation becomes:
[tex]t(n)=-729(\frac{1}{3}) ^{n-1}[/tex]
