Arithmetic sequence

 

The ninth and tenth terms of an arithmetic sequence are 1/4 and -1/3, respectively. What is the second term?   

 

Let's use a common denominator so all we have to worry about are the top numbers.    

 

Try 12 as the common denominator, which would be 3/12 and –4/12    

So it looks like the change from any term to the next term is –7/12.  

 

Let's work backwards, 10^th term, 9^th term, and keep adding 7/12 (since we're going backwards) 

 

10    -    –4/12     add 7/12 to this to get the 9^th term  

  9    -      3/12     add 7/12 to this to get the 8^th term  

  8    -    10/12  

  7    -    17/12  

  6    -    24/12  

  5    -    31/12  

  4    -    38/12  

  3    -    45/12  

  2    -    52/12     unless I've bungled terribly, 52/12 is the 2^nd term, or 4⁴/₁₂  which reduces to  4¹/₃  

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