University:
College
Course:
College Mathematics
Academic year:

2023
Views:

383

Pages:

2
Author:

J. Lay

Identifying Number Patterns. when looking Patterns in numbers, is often useful to take differences of the numbers you are provided. If the First differences are not constant, take differences again. When First differences Constant, the Patern represent a linear equation. In this case, the equation is: Y= 2x-5. The Constant difference Is the Coefficient of x in the equation. When second differences are constant, the pattern represents a quadratic equation. In the case, the equation is: Y = x²+1. The Constant difference, devided by 2, gives the Coefficient x² in the equation. when taking Successive differences yields Pattern that do not Seem to level out, the Pattern may be either exponen tial or recursive In the Pattern to the left, notice that the First and Second differences are the same. You might also notice that these differences are Successive Powers Of 2, This is typical For an exponential Pattern. In the case, the equationis: Y= 2+3, In the pattern to the left, notice that the First and Second differen ces appear to be repeating the original se quance, when this happens, the sequence may be recursive. This means that each new term is based on the terms before it. In the case the equation is: Yn= Yn-1 +Yn-2, meaning that to get each new term, you add the two terms before it.