Determine whether the sequence converges or diverges. if it converges, find the limit. An=3^(n+2)/(5^n)

An = [3^(n+2)]/(5^n)

=
[3^(n+2)]/[(3*5/3)^n]

=
[3^(n+2)]/[(3^n)*(5/3)^n]

=
(3^2)/[(5/3)^n]

= (5/3)^n

As
5/3 is greater than 1, as value of n increases,

the value
of (5/3)^n also increases,

and value of 9/(5/3)^n
decreases.

Therefore, sequences An
converges.

To find value of limit of
An:

When n approaches
infinity:

Value of limit (5/3)^n becomes
infinity

and  value of limit 9/(5/3)^n
becomes:

9/(infinity) =
0

Answer:

Limit An =
[3^(n+2)]/(5^n) as n approaches infinity is 0