- A sequence \(a _ { 1 } , a _ { 2 } , a _ { 3 } , \ldots\) is defined by
$$a _ { n } = \cos ^ { 2 } \left( \frac { \mathrm { n } \pi } { 3 } \right)$$
Find the exact values of
- \(a _ { 1 }\)
- \(a _ { 2 }\)
- \(a _ { 3 }\)
- Hence find the exact value of
50
$$n + \cos ^ { 2 } \frac { n \pi } { 3 }$$
You must make your method clear.