Answer:
The recursive formula of the geometric sequence is:
Step-by-step explanation:
A recursive formula is a formula using which every next term is based on the previous term.
Each next term of a geometric sequence can be determined when we multiply the previous term with a constant. That constant number is called a 'common ratio' which is denoted by 'r'.
Given the sequence
27, -9, 3, -1,...
Let us find the common ratio 'r' of all the adjacent terms
r = -9/27 = -1/3, r = 3/-9 = -1/3, r = -1/3
Thus, the common ratio is: r= -1/3
The recursive formula for the geometric sequence is:
aₙ = aₙ₋₁ (r)
Here,
aₙ represents the general term
aₙ₋₁ represents the previous term
'r' represents the common ratio
as
a₁ = 27
Substituting our values, we have
aₙ=aₙ₋₁(r)
Putting n=2 to get the second value
a₂=a₂₋₁(-1/3)
= a₁ (-1/3)
= 27 (-1/3)
= -9
Thus, the next term of a geometric sequence can be determined when we multiply the previous term with a constant.
Therefore, the recursive formula of the geometric sequence is:
