Answer: [tex]f(n)=19-7n[/tex]
Step-by-step explanation:
The explicit formula for an arithmetic sequence is given by :-
[tex]f(n)=a+(n-1)d[/tex] (1)
, where a = first term
d= common difference
n= number of term
The given arithmetic sequence = 12, 5, -2, -9..
First term : a = 12
Common difference : d= 5-12=-7 [Difference between any two consecutive terms.]
Put a = 12 and d= -7 in (1) , we get
[tex]f(n)=12+(n-1)(-7)[/tex]
Hence, the explicit formula for the given arithmetic sequence : [tex]f(n)=12+(n-1)(-7)[/tex]
We we solve it further , we get
[tex]f(n)=12-7n+7[/tex]
[tex]f(n)=19-7n[/tex]
Required explicit formula : [tex]f(n)=19-7n[/tex]
