- A sequence \(a _ { 1 } , a _ { 2 } , a _ { 3 }\) is defined by
$$a _ { n } = \sin ^ { 2 } \left( \frac { n \pi } { 3 } \right)$$
Find the exact values of
a. i) \(a _ { 1 }\)
ii) \(a _ { 2 }\)
iii) \(a _ { 3 }\)
b. Hence find the exact value of
$$\sum _ { n = 1 } ^ { 100 } \left\{ n + \sin ^ { 2 } \left( \frac { n \pi } { 3 } \right) \right\}$$