Challenging +1.2 This is a standard recurrence relation convergence problem requiring students to assume a_n+1/a_n → L, substitute into the recurrence to get L = 2 + 3/L, then solve the resulting quadratic. While it requires understanding of limits and algebraic manipulation, it's a well-practiced technique with clear steps and no novel insight needed. The 4 marks reflect routine application of a taught method.
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]
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]\\
\hfill \mbox{\textit{OCR MEI C4 Q6 [4]}}