6 A sequence is defined by $$a _ { n + 1 } = 2 a _ { n } + 3 a _ { n - 1 } \quad \text { with } a _ { 1 } = 1 \text { and } a _ { 2 } = 1 .$$ Using the method on page 5, show that the value to which the ratio of successive terms converges is 3 .
[0pt] [4]