5,-5,-15,-25,-35,...

Subtract the 2nd term minus the 1st term = (-5)-(5) = -5-5 = -10
Subtract the 3rd term minus the 2nd term = (-15)-(-5) = -15+5 = -10
Subtract the 4th term minus the 3rd term = (-25)-(-15) = -25+15 = -10
Subtract the 5th term minus the 4th term = (-35)-(-25) = -35+25 = -10

Yes it is an arithmetic sequence because all those differences are the 
same; therefore the common difference is -10 

-----------------------------------------------------

1,2,4,7,11,...

Subtract the 2nd term minus the 1st term = (2)-(1) = 1
Subtract the 3rd term minus the 2nd term = (4)-(2) = 2
Subtract the 4th term minus the 3rd term = (7)-(4) = 3
Subtract the 5th term minus the 4th term = (11)-(7) = 4

No it is not an arithmetic sequence, because these difference are not 
all the same.  So there is no common difference (Note: We could have 
stopped when we found that the 2 was not the same as the 1).

Edwin

 

Hi, 

Determine whether or not the following sequences are arithmetic.

If yes state the common difference.

{5,-5,-15,-25,-35,...}    || yes, d= -10

(1,2,4,7,11,...)  NO  

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