Given:
The arithmetic sequence:
[tex]7,3,-1,-5,...[/tex]
Required:
We need to find the nth term equation and value of 20 th term.
Explanation:
The first term of the given arithmetic sequence is a =7.
[tex]d=3-7=-4[/tex]
The common difference is d =-4.
Consider the nth term formula for the arithmetic sequence.
[tex]a_n=a+(n-1)d[/tex]
Substitute a =7 and d =-4 in the formula.
[tex]a_n=7+(n-1)(-4)[/tex]
[tex]a_n=7+n(-4)-1(-4)[/tex]
[tex]a_n=7-4n+4[/tex]
[tex]a_n=11-4n[/tex]
The equation for the nth term of the given sequence is
[tex]a_n=11-4n.[/tex]
Substitute n=20 in the equation to find the value of 20 th term.
[tex]a_{20}=11-4(20)[/tex]
[tex]a_{20}=11-80[/tex]
[tex]a_{20}=-69[/tex]
Final answer:
[tex]a_n=11-4n[/tex]
[tex]a_{20}=-69[/tex]
