Write the first six terms of the sequence given by : a1=a2=1 an=2*an-1 + 3*an-2, n>2 n n.n-1,n-2 is an index.

a1 = a2 =1

an = 2an-1 +3an-2 
n > 2.

Applying the relation, for n
=3,4,5,6

a3 = 2a2+3a1 =2+3 =
5,

a4 =2a3+3a2 = 2*5 +3*1 =
13

a5 = 2a4+3a3 = 2*13+3*5
=41

a6 = 2a5+3a4 = 2*41+3*13 =
121.

So 1,   1,   4,    13,   41, and 121  are the first 6
terms.