Question

The recursive rule for a geometric sequence is given.

Answer 1

Answer:

an = 2/5 * (5) ^ (n-1)

Step-by-step explanation:

The common ratio is 5

(That is the number we multiply by)

The formula is

an = a1 (r) ^ (n-1)

an = 2/5 * (5) ^ (n-1)

Answer 2

Answer:

$a_n= \frac{2}{5} (5)^{n-1}$

Step-by-step explanation:

The recursive rule for a geometric sequence is given.

a1= 2/5; an=  $5a^{n-1}$

a1 is the first term = 2/5

USe the recirsive rule. compare an=  $ra^{n-1}$, where 'r' is the common ratio with the given recursive formula

r= 5, common ratio is 5

General explicit rule

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

a1=2/5  and r= 5

So explicit rule becomes

$a_n= \frac{2}{5} (5)^{n-1}$