Modelling
Overview of Modelling

Modelling is a method used to express realworld scenarios or abstract concepts using mathematical terms or equations.

It’s a vital tool for problemsolving, providing a way to step back from the complexity of a situation and understand it from a different perspective.

Sequences and series can be used to model a variety of situations such as the growth of a population or the sum of a series of payments.
Fundamental Concepts

A sequence is a list of numbers or objects in a particular order.

A series is the sum of the terms of a sequence.

Both sequences and series can be either finite or infinite.

Understanding the nature of a sequence or series and how it behaves over time is critical in accurately modelling a given situation.
Mathematical Models and RealWorld Scenarios

Mathematical models help in representing, analysing, and predicting the behaviour of realworld scenarios.

For instance, an arithmetic sequence can be used to model a situation where a fixed amount gets added or subtracted at each step, like the monthly increase of a salary.

A geometric sequence can be used to model exponential growth or decay, such as the spread of an infectious disease or the depreciation of a car’s value over time.
Formulation of Mathematical Models

To create a mathematical model, start by understanding the details and constraints of the situation.

Identify the sequence or series that best represents the situation.

Define the first term, the common difference (for an arithmetic series), or the common ratio (for a geometric series).

Construct a general formula that represents the series or sequence in the model.
Predictions and Interpretations

Mathematical models enable predictions about future conditions or events.

In sequences and series, these predictions might include forecasting the nth term or calculating the sum of a series to a particular point.

It’s crucial to remember that whilst these models provide useful approximations, they may not account for all variables and factors in realworld situations.
Verification and Adjustment of Models

After formulating the model, verify its accuracy by comparing predictions with actual outcomes.

If the model’s predictions are inconsistent with realworld results, adjustments to the model’s parameters or assumptions may be required.

This process of iteration and refinement helps increase the accuracy and applicability of the model.
Applications of Modelling

Applications of modelling with sequences and series span diverse fields such as economics, physics, ecology, and engineering.

Mastering the art of modelling can significantly enhance problemsolving skills and open up opportunities for further explorations in mathematics.
Importance of Modelling in Problem Solving

Modelling provides a concrete, simplified representation of complex or abstract concepts.

It enables better comprehension, interpretation, and solutions to potentially intricate problems.

Developing sophisticated modelling skills is pivotal for future exploration in mathematics and related disciplines.