Given:
First term of an arithmetic sequence = 5
Second term = 3
To find:
The explicit formula for the given arithmetic sequence.
Solution:
We have,
First term: [tex]a_1=5[/tex]
Second term: [tex]a_2=3[/tex]
Common difference is
[tex]d=a_2-a_1[/tex]
[tex]d=3-5[/tex]
[tex]d=-2[/tex]
Now, the explicit formula for an arithmetic sequence is
[tex]a_n=a+(n-1)d[/tex]
where, a is first term and d is common difference.
Putting a=5 and d=-2, we get
[tex]a_n=5+(n-1)(-2)[/tex]
It can also be written as
[tex]a_n=5-2n+2[/tex]
[tex]a_n=7-2n[/tex]
Here, n is an integer greater than or equal to 1.
Domain is the set of input values.
Therefore, the explicit equation is [tex]a_n=5+(n-1)(-2)[/tex] or [tex]a_n=7-2n[/tex] and domain is all interest greater than or equal to 1.
