Question

A recursive rule for a geometric sequence is a1=4/9;an=3an−1

Answer 1

The answer is (4/9)(3)^n-1

Answer 2

Answer:

Explicit rule for this sequence is, $a_n = 49\cdot (3)^{n-1}$

Step-by-step explanation:

A recursive rule for a geometric sequence is $a_1=49$, $a_n = 3a_{n-1}$

First term $a_1= 49$

To get second term, just multiply the first term by 3

$a_n = 3 a_{n-1}$

$a_2 = 3 a_1$

$a_2= 3\cdot 49$

so, we get the common ratio r = 3

Now, Explicit rule for geometric sequence is given by:

$a_n = a_1 \cdot (r)^{n-1}$

Here, $a_1= 49$ and r= 3

So, explicit rule is :

$a_n = 49\cdot (3)^{n-1}$