Question on Finding the Value of x bu Iteration Method

Topic : Iteration Method of Solving an Expression and Finding the Value of x.

Question : Solve x = 0.5x + 3 by using the iteration method.

Answer :

x = .5x +3

let the first iteratioin be x = 1

then

x = .5 (1) +3 = 3.5

x = .5 (3.5) +3 = 4.75

x = .5 (4.75) +3 = 5.375

x = .5 (5.375) +3 = 5.6875

x = .5 (5.6875) +3 = 5.84375

x = .5 (5.84375) +3 = 5.921875

x = .5 (5.921875) +3 = 5.96093

x = .5 (5.96093) +3 = 5.9804

x = .5 (5.9804 ) +3 = 5.99023

x = .5 (5.99023 ) +3 = 5.99511

x = .5 (5.99511 ) +3 = 5.99755

hence we can say that the solution is approximately 5.99

infact the exact root is x=6, which can be found solving the given equation

Hope the Method Explained will do the needful.