Question

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

What is the recursive rule for the sequence?
1) an=−2(an+1)
a1=5
2) an=−5(an+1)
a1=2
3) an=−2(an−1)
a1=5
4) an=−5(an−1)
a1=2

Answer 1

3) an=−2(an−1)

a1=5

Explanation:

Answer 2

3)
`a_n=-2a_(n-1)`,
`a_1=5`

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`