2,5,2,9,2,13,2,17,...

The sum of the 50 odd numbered terms 

2,_,2,_,2,_,2,_,...2

is 50*2 = 100  <--sum of odd numbered terms (all 2's)

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The sum of the 50 even-numbered terms:

5,__,9,__,13,__,17,__,...

That's 50 terms of an arithmetic sequence with common difference 4:











  <--sum of even-numbered terms.

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Add them together = 100 + 5150 = 5250  <--answer

Edwin