If a, start subscript, 1, end subscript, equals, 4a
1
​
=4, a, start subscript, 2, end subscript, equals, 3a
2
​
=3 and a, start subscript, n, end subscript, equals, 3, a, start subscript, n, minus, 1, end subscript, plus, 2, a, start subscript, n, minus, 2, end subscripta
n
​
=3a
n−1
​
+2a
n−2
​
then find the value of a, start subscript, 6, end subscripta
6
​
.