Question

The explicit rule for a sequence is an=9(−5)n−1 .

What is recursive rule for the sequence?




an=5−(an−1),a1=9

an=−9(an−1),a1=5

an=9−(an−1),a1=5

an=−5(an−1),a1=9

Answer 1

Option 4th is correct.

`a_n = -5 \cdot a_(n-1)` ,
`a_1 = 9`

Explanation

The explicit sequence of the geometric sequence is given by:

`a_n = a_1r^(n-1)` ....[1]

where,

r is the common ratio

n is the number of terms

`a_1` is the first term

As per the statement:

The explicit rule for a sequence is:

`a_n=9(-5)^(n-1)`

On comparing [1] we have;

`a_1 = 9` and r= -5

Recursive formula for the geometric sequence is given by:

`a_n = r \cdot a_(n-1)` for
`n\geq 2`

Substitute the given values we have;

`a_n = -5 \cdot a_(n-1)`

Therefore, the recursive rule for the sequence is,
`a_n = -5 \cdot a_(n-1)` ,
`a_1 = 9`

Answer 2

Explicit rule is a(n) = 9*(-5)^(n-1)

The recursive rule is a(n) = -5*a(n-1); a(1) = 9

The first term is 9. Each new term is found by multiplying the previous term by -5

We can see this when we raise -5 to a whole number power. Eg: 9(-5)^3 = 9*(-5)*(-5)*(-5)

Answer: Choice D