Question

?? So lost with this

Answer 1

Answer:

$A)\ 1,\ -1,\ -3\\\\B)\ d=-2\\\\C)\ \left\{\begin{array}{ccc}a_1=11\\a_n=a_{n-1}-2\end{array}\right\\\\D)\ f(n)=-2n+13$

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:

$\left\{\begin{array}{ccc}a_1=11\\a_n=a_{n-1}-2\end{array}\right$

D) Explicit Function:

$f(n)=a_1+(n-1)d$

a₁ - first term

d - common difference

Substitute a₁ = 11 and d = -2:

$f(n)=11+(n-1)(-2)=11-2n+2=-2n+13$