bearing in mind that an explicit form is simply the sequence written as a function of some variables, so we simply simplify and add like-terms.
[tex]\bf a_n=(-1)+(n-7)(-4)\implies a_n=-1+(-4n+28)\implies a_n=27-4n[/tex]
Answer:
The explicit formula of the given sequence
[tex]a_n=27-4n[/tex]
Step-by-step explanation:
Given A sequence is in an arthmetic progression
The recursive formula
[tex]a_n=(-1)+(n-7)(-4)[/tex]
Recursive formula:It is the formula to find the value of [tex]n^{th}[/tex] term ([tex]a_n[/tex] ) of the sequence when [tex](n-1)^{th}[/tex] term of the sequence is known .
Explicit formula:It is the formula to find the value of any term of the sequence when [tex]n^{th}[/tex] term is known.
[tex]a_n= -1-4n+28[/tex]
By simplification
[tex]a_n= 27-4n[/tex]
By simplification
Hence, the explicit formula ,[tex]a_n=27-4n[/tex].
