Find an explicit formula for the recursively defined sequenc

Find an explicit formula for the recursively defined sequence a_n = 2a_n - 1 + 3 a_n - 2, n greaterthanorequalto 2, given a_0 = 3 and a_1 = 17.

Solution

a0=3

a1=17;

a2=2*a1+3*a0=2*17+3*3=34+9=43,

a3=2*43+3*17=137

a4=2*137+3*43=403

a5=2*403+3*137=1217

This sequence is neither arithmetic nor geometric. It does, however, have a pattern of development based upon each previous term.