Recursive sequences

Question

what is the recursive formula for the following two sequences?

3 -9 27 -81 ….

2 ½ 2 ½ 2 ½ ….

Answer 1

an = -3an-1

each term, an is -3 times the previous term, an-1

a1 =3

an= a1(r^(n-1)

an = 3(-3)^(n-1)

3,-9,27,-81, ...

for 2 1/2, 2 1/2, 2 1/2, ...

an = an-1

an = a1 = 2 1/2

an = 2 1/2

the first sequence is geometric with common ratio, r, = -3, 1st term, a1 = 3

the 2nd sequence could be treated either arithmetic with a common difference, d =0

or a geometric sequence with common ratio, r =1

a1 = 1st term = 2 1/2