Respuesta :
Answer:
[tex]a_n=\frac{-1}{2}a_{n-1}[/tex]
[tex]a_1=2[/tex]
Step-by-step explanation:
The recursive rule is a term defined in terms of other terms in the sequence.
The is a geometric sequence because it has a common ratio.
The common ratio can be found by dividing a term by previous term.
For example, all of these are equal:
[tex]\frac{-1}{2}[/tex]
[tex]\frac{\frac{1}{2}}{-1}[/tex]
[tex]\frac{\frac{-1}{4}}{\frac{1}{2}}[/tex]
They are all equal to [tex]\frac{-1}{2}[/tex].
So we are saying:
[tex]\frac{\text{term}}{\text{previous term}}}=\frac{-1}{2}[/tex]
More formally:
[tex]\frac{a_n}{a_{n-1}}=\frac{-1}{2}[/tex].
Multiply both sides by [tex]a_{n-1}[/tex]:
[tex]a_n=\frac{-1}{2}a_{n-1}[/tex]
When doing recursive form, you need to state a term of the sequence (or more depending on the recursive form you have).
So the first term is 2.
So the full thing for the answer is:
[tex]a_n=\frac{-1}{2}a_{n-1}[/tex]
[tex]a_1=2[/tex]
