Question

Devise an iterative algorithm to find the nth term of the sequence defined in Exercise 29.

Short answer

The recursive algorithm is,

a := 1

b := 2

if n = 0 return b

else\for i = 1 to n - 1

c: = a.b

a := b

b := c return c

Step-by-step solution

Consider the following algorithm

The recursive algorithm is,

procedure term (n : positive integers)

if n = 0 then

return 1

else if n = 1 then

else return term (n - 1) . term (n - 2)

Give an iterative algorithm to find the nth term of the sequence defined in Exercise 29

Devise an iterative algorithm to find the $n^{th}$term of the sequence defined by $a_0=1$and ${\mathrm{a}}_1=2\mathrm{for}\mathrm{n}=2,3,4,.....$

a := 1

b := 2

if n = 0 return b

else\for i = 1 to n - 1

c: = a.b

a := b

b := c return c

Hence, the required algorithm is shown above.