The explicit rule for a sequence is an=7(−4)n−1.What is the recursive rule for the sequence? an=−4(an−1),a1=7 an=−7(an−1),a1=4 an=−7(an+1),a1=4 an=−4(an+1),a1=7

The correct answer is

[tex]a_n=-4(a_{n-1}), a_1=7[/tex]

The explicit formula is of the form
[tex]a_n=a_1(r)^{n-1}[/tex], 
where a₁ is the first term and r is the common ratio.  Comparing this to our explicit form, we see that r = -4 and a₁ = 7.

The recursive formula is of the form
[tex]a_n=a_{n-1}*r[/tex]; using r=-4 gives us
[tex]a_n=-4(a_{n-1}), a_1=7[/tex]