Question

The explicit rule for a sequence is given.

Answer 1

Answer:

$a_1=3$

$a_n = 16 \cdot a_{n-1}$

Step-by-step explanation:

The explicit formula for the geometric sequence is given by:

$a_n =a_1 \cdot r^{n-1}$      ....[1]

where

$a_1$ is the first term

r is the common ratio of the consecutive terms

n is the number of terms

Given that:

The explicit rule for a sequence is given. by:

$a_n =3 \cdot (16)^{n-1}$

On comparing with equation [1] we have;

$a_1=3$ and r = 16

Use the recursive formula for the geometric sequence is:

$a_n = r \cdot a_{n-1}$

Substitute the given values we have;

$a_n = 16 \cdot a_{n-1}$

therefore, the recursive rule for the geometric sequence is, $a_n = 16 \cdot a_{n-1}$

Answer 2

$a_{1}=3$

$a_{n}=16a_{n-1}$

just use the standart recursive for geometric sequence