Question

Find the first three terms of the sequence described by the following recursive formula:
an = 3an – 1 + 2 where a4 = 20

a1 =
a2 =
a3 =

Answer 1

We have a_n = 3a_{n-1} + 2, so a_{n-1} = (a_n - 2)/3. Given a4 = 20:

a3 = (20 − 2)/3 = 18/3 = 6
a2 = (6 − 2)/3 = 4/3
a1 = (4/3 − 2)/3 = (−2/3)/3 = −2/9

Thus:
a1 = −2/9, a2 = 4/3, a3 = 6.