Question-75

Question-75

Give a recursive definition of the sequence {a_n} , n = 1, 2, 3, …… if

 a)     a_n = 4n – 2.

 b)    a_n = 3 + 3.(-1)ⁿ.

c)      a_n = n(n + 2).

d)    a_n = 2n^2.

 

Solution

a)  a₁ = 2 and a_{n + 1} = a_n + 4 for all n 1

 

b) a₁ = 0 , a₂ = 6 and a_n = a_n – 2 for all n 3

 

c)  a₁ = 3 and a_n = a_{n – 1} + 2n + 1 for all 2

 

d) a₁ = 2 and a_n = a_n – 1 + 4_n – 2 for all n 2