Question

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

Answer 1

Answer:

Option 4th is correct.

$a_n = -5 \cdot a_{n-1}$ , $a_1 = 9$

Step-by-step 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