sequences

 

What is the 2009th term in the arithmetic sequence whose first four terms are 2, 10, 18, 26?      

 

Let's see if we can get a little pattern going here 

 

We can see that the increment is 8, so, tabulating    

 

Term

Number (n)         Value    

 

         1                 2 + (8)(1 – 1)    

         2                 2 + (8)(2 – 1)    

         3                 2 + (8)(3 – 1)    

         4                 2 + (8)(4 – 1)    

         n                 2 + (8)(n – 1)    

   2009                 2 + (8)(2009 – 1)    

 

The 2009^th term therefore is 16,066    

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