Answer:
3) [tex]a_n=-2a_{n-1}[/tex], [tex]a_1=5[/tex]
Step-by-step explanation:
Given that the explicit rule for a sequence is [tex]a_n=5(-2)^{n-1}[/tex].
Now we need to find about what is the recursive rule for the sequence and match with the given choices to find the correct choice.
1) [tex]a_n=-2a_{n+1}[/tex], [tex]a_1=5[/tex]
2) [tex]a_n=-5a_{n+1}[/tex], [tex]a_1=2[/tex]
3) [tex]a_n=-2a_{n-1}[/tex], [tex]a_1=5[/tex]
4) [tex]a_n=-5a_{n-1}[/tex], [tex]a_1=2[/tex]
Plug n=1 into given formula to get first term
[tex]a_n=5(-2)^{n-1}[/tex]
[tex]a_1=5(-2)^{1-1}=5(-2)^{0}=5(1)=5[/tex]
base of the exponent part is (-2) so that means we need to multiply -2 to the previous term to get nth term
Hence correct choice is: 3) [tex]a_n=-2a_{n-1}[/tex], [tex]a_1=5[/tex]
