Answer:
Explicit form is f(n) = (-1)ⁿ⁻¹
Recursive form of sequence is given by f(n) = -f(n-1)
Step-by-step explanation:
We can see that 1, −1, 1, −1, 1, −1, … is a geometric sequence with common ration -1 and first term 1.
Explicit form is given by
f(n) = arⁿ⁻¹
f(n) = 1 x (-1)ⁿ⁻¹ = (-1)ⁿ⁻¹
Explicit form is f(n) = (-1)ⁿ⁻¹
The explicit form of sequence is given as
f(n) = (-1)ⁿ⁻¹
So nth term is given by
f(n) = (-1)ⁿ⁻¹
(n-1)th term is given by
f(n-1) = (-1)ⁿ⁻²
We have
[tex]\frac{f(n)}{f(n-1)}=\frac{(-1)^{n-1}}{(-1)^{n-2}}=(-1)^{n-1-n+2}=-1\\\\f(n)=-f(n-1)[/tex]
Recursive form of sequence is given by f(n) = -f(n-1)
