6. Five marks exercie problems III

1. Find the indicated terms of the sequences whose \(n^{th}\) terms are given by

 

(i) \$a_n=\frac{5n}{n+2}$; (a_6\) and \(a_{13}\)

 

\(a_6\) \(=\) $\frac{i}{i}$ and \(a_{13}\) \(=\) $\frac{i}{i}$

 

 

(ii) $a_n=-\left(n^2-4\right)$; \(a_4\) and \(a_{11}\)

 

\(a_4\) \(=\) $i$ and \(a_{11}\) \(=\) $i$

 

 

2. If \(a_1 = 1\) and \(a_2 = 1\) and \(a_n = 2a_{n - a} + a_{n - 2}\), \(n \ge 3\), \(n \in \mathbb{N}\), then find the first six terms of the sequence.