Answer:
[tex]A)\ 1,\ -1,\ -3\\\\B)\ d=-2\\\\C)\ \left\{\begin{array}{ccc}a_1=11\\a_n=a_{n-1}-2\end{array}\right\\\\D)\ f(n)=-2n+13[/tex]
Step-by-step explanation:
It's an arithmetic sequence.
9 = 11 - 2
7 = 9 - 2
5 = 7 - 2
3 = 5 - 2
A) next three terms: 3 - 2 = 1, 1 - 2 = -1, -1 - 2 = -3
B) Common difference = -2
C) Recursive Function:
[tex]\left\{\begin{array}{ccc}a_1=11\\a_n=a_{n-1}-2\end{array}\right[/tex]
D) Explicit Function:
[tex]f(n)=a_1+(n-1)d[/tex]
a₁ - first term
d - common difference
Substitute a₁ = 11 and d = -2:
[tex]f(n)=11+(n-1)(-2)=11-2n+2=-2n+13[/tex]
