There is a sequence of numbers a1, a2, ... where a1 = 2, a2 = 3, and an =  
an-1
an-2
  for n ≥ 3. What is the value of a756 ?


Answer:

 

2
3
 

Step by Step Explanation:
  1. A series of number is given. Where a1 = 2 a2 = 3 and an =  
    an-1
    an-2
      for n ≥ 3.
  2. On relating the sequence, a1 = 2
    a2 = 3
    a3 =  
    a2
    a1
      =  
    3
    2
     
    a4 =  
    a3
    a2
      =  
    1
    2
     
    a5 =  
    a4
    a3
      =  
    1
    3
     
    a6 =  
    a5
    a4
      =  
    2
    3
     
    a7 =  
    a6
    a2
      = 2
    a8 =  
    a7
    a6
      = 3
    and so on....
  3. Therefore, we will get a sequence which repeat after every sixth term,
    i.e. a1 = 2, a2 = 3, a3 =  
    3
    2
     , a4 =  
    1
    2
     , a5 =  
    1
    3
     , a6 =  
    2
    3
     , a7 = 2, a8 = 3 ....
  4. As we have to find out a756. On dividing 756 by 6 which leaves a remainder of 0. So this term is equivalent to 6th term i.e. a6.
  5. Thus, a756 = a6 =  
    2
    3
     .

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