Question

Write a recursive formula for the sequence
1, 3, 9, 27, 81, . . . a1 = 1
an = 3an - 1
an = 3n
an = 3n - 1
an = 3an + 1

Answer 1

the first one \[\huge a_n=3a_{n-1}\]

Answer 2

however, to my class, we must prove it by induction. I don't know whether you need or not, since you just ask for formula.