Question

A sequence of numbers is formed by the iterative process

3/Un+1
U1 = 4

U2=
U3=

Answer 1

3/5, 1/2

Explanation:

u(1) = 4 (given)

3 3

u(2) = ----------- = ------- where u(1) = 4 and u(1) + 1 = 5

4 + 1 5

3

u(3) = -------- = 3/6 = 1/2

5+1

Answer 2

The value of u₂ is 3/4.

The value of u₃ is 4.

The iterative process is given by the formula:

Un+1 = 3/Un

U₁ = 4

To find the value of U₂, we can substitute n = 1 into the formula:

U₂ = 3/U₁ = 3/4

To find the value of U₃, we can substitute n = 2 into the formula:

U₃ = 3/U₂ = 3/(3/4) = 4

Therefore, the values of U₂ and U₃ are:

U₂ = 3/4

U₃ = 4

The correct answers are:

a. 3/4

b. 4