Question

How can you use an equation to make a prediction from a pattern?

Answer 1

Let's say your pattern is 5, 10, 15. You can do 10 divided by 5 which equals 2 then you can do 15 divided by 5 which equals 3. This means that the pattern increase by one. 1 times 5 equals 5. 2 times 5 equals 10. And that 3 times 5 equals 15. This way you know that the fourth number will be 4 times 5. Another way you can do is use an exponential or linear equation to find a pattern. Take the second number and divide it be the first number. Take then answer and times it by what number you need to fine. So let's say that number that you had founded was 6 and the pattern number you need is 8. So then you do 8 times 6 while will get you 48. If you need to know more I would google how to do exponential equations or linear.

Answer 2

Upon formation of an equation from a given pattern, we know how the variables in the patter are related. Using the equation, we can find the value of one of the missing variables if the rest are known and also predict the values of the pattern at given conditions.
An example:
y = 2x + 5
if we are to predict the value of y at x = 3, we simply substitute 3 into x
y = 2(3) + 5
= 11