State if the following is true or false.

In following situation, the list of numbers involved arithmetic progression.

Number of pairs of rabbits in successive months when the pair of rabbits is too young to produce in their first month. In the second month and every subsequent month, they produce a new pair. Each new pair of rabbits pr a new pair in their second months and every subsequent month (see Fig.) (assume that no rabbit dies).

Question

State if the following is true or false.

In following situation, the list of numbers involved arithmetic progression.

Number of pairs of rabbits in successive months when the pair of rabbits is too young to produce in their first month. In the second month and every subsequent month, they produce a new pair. Each new pair of rabbits pr a new pair in their second months and every subsequent month (see Fig.) (assume that no rabbit dies).

Accepted Answer

Given figure is,According to the question, The number of pairs of rabbit at the start of the

1
    
     st
   
   month=1
  The number of pairs of rabbit at the start of the

2
    
     nd
   
   month=1
  The number of pairs of rabbit at the start of the

3
    
     rd
   
   month=2
  The number of pairs of rabbit at the start of the

4
    
     th
   
   month=3
  The number of pairs of rabbit at the start of the

5
    
     th
   
   month=5
  Therefore, the series is 1,1,2,3,5,....Now, the common difference will be,⇒a2-a1=1-1⇒a2-a1=0Again,⇒a3-a2=2-1⇒a3-a2=1 Difference between the 3rd and the 2nd term is not equal to the difference between the 2nd and 1st term. Hence, it doesn’t form an AP.The list of numbers doesn’t form an arithmetic progression.Therefore, the statement is false.Hence, option 2 is correct.

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