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In the sequence of numbers 1, 4, 3, ... each term after the first two is calculated as the term preceding it minus the term preceding that. So, for example, the third term is the second term minus the first term, i.e. 3 = 4 - 1. What is the sum of the first 2014 terms of the sequence?

 May 24, 2018

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 #1
avatar+130071 
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Notice the pattern : 

 

1, 4, 3, -1, -4, -3, 1, 4, 3, -1, -4, -3

 

The series has a cycle of 6.....and the sum of these terms  = 0

 

So

 

2014 mod 6 =  4

 

So we will have   2010/6  = 335 of these cycles  and  the last  4 terms after that are   1,4,3  -1

 

So....the sum  =  7

 

 

 

cool cool cool

 May 24, 2018

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