# Group Sequence

Number Theory Level pending

Consider following sequence:

$$1 ,\quad \frac { 1 }{ 2 } ,\quad 1 ,\quad \frac { 1 }{ 3 } ,\quad \frac { 2 }{ 3 } ,\quad 1 ,\quad \frac { 1 }{ 4 } ,\quad \frac { 1 }{ 2 } ,\quad \frac { 3 }{ 4 } ,\quad 1 ,\quad \frac { 1 }{ 5 } ,\quad \frac { 2 }{ 5 } ,\quad \cdots \cdots$$

1. Find 100th term in the sequence.

2. Where is $$\frac { 8 }{ 17 }$$ in this sequence (which term)?

Let the answer of first question be $$\frac { a }{ b }$$ where a and b are coprime, and answer of second question be $$c$$.

Evaluate $$\boxed{a+b+c}$$

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