Number of pairs of rabbits in successive months when the pair of rabbits is too young to produce in their first month.

Question

In which of the following situations does the list of numbers involved arithmetic progression, and why?

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).

Answer 1

Assuming that no rabbit dies,

the number of pairs of rabbits at the start of the 1^st month = 1

the number of pairs of rabbits at the start of the 2^nd month = 1

the number of pairs of rabbits at the start of the 3^rd month = 2

the number of pairs of rabbits at the start of the 4^th month = 3

the number of pairs of rabbits at the start of the 5^th month = 5

Therefore, the series is

1, 1, 2, 3, 5, 8,…

Difference between 2^nd and 1^st term = 1 – 1 = 0

Difference between 3^rd and 2^nd term = 2 – 1 = 1

Since, the difference is not same.

Therefore, the number of pair of rabbits in successive months are 1,1,2,3,5,8,… and they don’t form an AP.