Question
An iterative formula is shown below. x_(n+1)=(x_(n))/(2)+(1)/(x_(n)) Starting with x_(1)=10 work out the values of x_(3) and x_(4) Give your answers to 1 d.p.
Answer
4.7
(291 Votes)
Yasmin
Professional · Tutor for 6 years
Answer
1. Plugging the given value
for
into the iterative formula gives us the second term,
:
. 2. Now, substitute
(truncated to 1 decimal place) into the iterative formula to find
:
.3. Substitute
(truncated to 1 decimal place) into the iterative equation to find
:
and
each to 1 decimal place.
Explanation
This question essentially involves a mathematical concept known as iteration, which involves creating new (better) predictions (or terms) according to a mathematical process or formula. The given formula is
Here, our initial term,
, is given as 10. The iterative formula indicates using the preceding number to get the next. Starting with
, you can then use the formula to find
, then
, then
, and so on, with:1.
.2.
.3.
.Note Every subsequent value depends on the value of the previous one.