Question-75

Question-75

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

 a)     an = 4n – 2.

 b)    an = 3 + 3.(-1)n.

c)      an = n(n + 2).

d)    an = 2n2.

 

Solution

a)  a1 = 2 and an + 1 = an + 4 for all n \geq1

 

b) a1 = 0 , a2 = 6 and an = an – 2 for all n \geq 3

 

c)  a1 = 3 and an = an – 1 + 2n + 1 for all \geq 2

 

d) a1 = 2 and an = an – 1 + 4n – 2 for all n \geq 2

 

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