Simple Series

Calculus Level 3

For sequence \[ \left\{ { a }_{ n } \right\} \], the following holds: \[ { a }_{ 1 }=5 \] and \[ { a }_{ 100 }=200 \]. Evaluate \[ \sum _{ k=1 }^{ 99 }{ { a }_{ k } } -\sum _{ k=1 }^{ 50 }{ { a }_{ 2k } } -\sum _{ k=1 }^{ 49 }{ { a }_{ 2k+1 } } \]

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