Question

The explicit rule for a sequence is given.

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

Enter the recursive rule for the geometric sequence.

a1= ______ ; an=______

Answer 1

Answer: a1=2/5 and an= 5an-1

Just took the test, you're welcome

Answer 2

`a_(1) =(2)/(5)` ,Recursive formula is :

`a_(n) =a_(n-1) .5`

Explanation:

To find a1 we put n=1 in the given Geometric sequence :

`a_(1) =(2)/(5)5^(1-1)`

`a_(1) =(2)/(5)`

`a_(2) =(2)/(5)5^(2-1) = 2`

Common difference = 2÷
`(2)/(5)` = 5.

r=5.

Recursive formula for a geometric sequence is

`a_(n) =a_(n-1) .r`

Recursive formula is :

`a_(n) =a_(n-1) .5`