Question

The explicit rule for a sequence is an=5(−2)^n−1

Answer 1

Answer:

3) $a_n=-2a_{n-1}$, $a_1=5$

Step-by-step explanation:

Given that the explicit rule for a sequence is $a_n=5(-2)^{n-1}$.

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) $a_n=-2a_{n+1}$, $a_1=5$

2) $a_n=-5a_{n+1}$, $a_1=2$

3) $a_n=-2a_{n-1}$, $a_1=5$

4) $a_n=-5a_{n-1}$, $a_1=2$

Plug n=1 into given formula to get first term

$a_n=5(-2)^{n-1}$

$a_1=5(-2)^{1-1}=5(-2)^{0}=5(1)=5$

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) $a_n=-2a_{n-1}$, $a_1=5$