HELP!!
given the sequences 1,5,25,125,...
write the explicit rule.
write the recursive rule.

Explicit:

a(n) = (5^n)/5

Recursive:

a(n) = 5 × a(n-1)

Step-by-step explanation:

1, 5, 25, 125...

1, 1×5 = 5, 5×5 = 25, 25×5 = 125..

It is a Geometric sequence with:

First term: 1

Common ratio: 5

Nth term of a Geometric sequence is:

a(n) = a(1) × r^(n-1),

Where a(1) is the first term and r is the common ratio.

Therefore,

a(n) = 1 × 5^(n-1)

a(n) = 5^n × 5^-1

a(n) = (5^n)/5

Recursive:

a(n) = 5 × a(n-1)