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In the sequence of numbers 3, 5, 2, ... 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. 2 = 5 - 3. What is the sum of the first 2014 terms of the sequence?

 Jun 18, 2022
 #1
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Your sequence will look like this:

 

3, 5, 2, - 3, - 5, - 2, 3, 5, 2, - 3, - 5, - 2, 3, 5, 2, - 3, - 5, - 2, 3.........2014th term will be a "3". The rest of them all cancel out.

 

Therefore, the sum of the first 2014 terms ==3.

 Jun 18, 2022
 #2
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I get the following last 4 terms:

 

3, 5, 2, - 3 ==7 as the sum of 2014 terms of this sequence.

 Jun 19, 2022

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