Question

An iterative formula is shown below.

Xn+1
Starting with 1
=
1
xn
+3
5, calculate the value of 3.
Give your answer to 2 d.p.

Answer 1

The answer is,

`x_3 = 3.31`

Explanation:

We are given the formula,

`x_(n+1) = (1/x_(n)) + 3`

Now,

`x_1 = 5\\Then, finding \ x_2,\\using \ the \ formula,\\x_2 = 1/x_1 + 3\\x_2 = 1/5 + 3\\x_2 = 1/5 + 15/5\\x_2 = (1+15)/5\\x_2 = 16/5\\`

Now, we find x_3,

Again, using the formula,

`x_3 = 1/x_2 + 3\\since, x_2 = 16/5, we \ get,\\x_3 = 1/(16/5) + 3\\x_3 = 5/16 + 3\\x_3 = 5/16 + 48/16\\x_3 = (5+48)/16\\x_3 = 53/16`

To 2 decimal points we get,

`x_3 = 3.31`