Sequences and Series Formulas: Discover their True Power

If you look around in your surroundings, you will find a number of patterns in nature – leaves and flowers with similar structures, the ripples on a lake, the symmetry of a starfish and many more patterns that don’t cease to amaze us. Nature inspired mathematicians to try and explain these patterns in nature; to work on mathematical models and understand the basics of geometric shapes and structures. Lot of work has been carried out in the field of number sequences and series to predict the possibility of an event, designing structures and buildings, analysis of real-life situations etc.

Mathematical sequences and series are also used in business and financial analysis to assist in decision-making and find the best solution to a given problem. (To understand the mathematical representations and details of number sequences and series formulas, take this basic course on statistics and probability.) Organizations use quantitative analysis in risk assessment and management, making investment decisions, pricing and many more important functions. If you are a business analyst, a statistician or an investment manager, your work will revolve around number patterns and the analysis of these patterns. So, let’s try and understand what exactly these numbers are and why are they so special?

What are Sequences and Series?

A Sequence is simply defined as a set of numbers that are in a particular order. For example, a sequence of even numbers will be (2, 4, 6, 8 …). If a sequence goes on forever, like the one mentioned, then it’s called an infinite sequence. However, if we say, ‘sequence of the first four even numbers’, then it will be a finite sequence that looks like this – (2, 4, 6, and 8)

A Series, on the other hand is the sum total of the numbers in a sequence and they too will be either infinite or finite in nature. In our above given example, the finite series will be the Summation ∑ (2+4+6+8) whereas the infinite series will be the Summation ∑ (2+4+6+8+…).

Examples of Sequences and Series

There are numerous mathematical sequences and series that arise out of various formulas. The arithmetical and geometric sequences that follow a certain rule, triangular number sequences built on a pattern, the famous Fibonacci sequence based on recursive formula, sequences of square or cube numbers etc. Series like the harmonic series, alternating series, Fourier series etc. have great importance in the field of calculus, physics, analytical functions and many more mathematical tools. They are widely used to in computer science, engineering, finance and economics etc. to determine various possibilities of a certain situation or criteria to design, analyze, build or predict something.

Importance of Sequences and Series

Did you know that the behavior of your company stocks in the financial markets follow a certain sequence? Or for that matter, you can predict how long it will take for your financial assets to double in market value? With the help of number sequences and series formulas, you can perform Quantitative Analysis, Financial and Business Analysis to help you in important business and investment decisions.

Quantitative Analysis

The method of understanding behavior and patterns in the real world by using mathematical models, measurement techniques and research is called Quantitative Analysis. It uses analysis of numbers and statistics to conduct functions like performance evaluation, financial analysis, predict behavior of markets and various other calculations.

It’s widely used by managers and business executives to handle complex business situations like risk analysis, forecasting and data analysis, competitive analysis etc. and find solutions to practical problems. Learn more about quantitative data analysis with this course.

Main Elements of Quantitative Analysis

The main purpose of quantitative analysis is to establish the relationship between one variable element and another. It uses logic, statistical data and reasoning to arrive at the results. Its main features are:

• Data is gathered using a structured research element like polls, surveys etc. from large groups of people representing the various sections of society.
• Objectives are clearly defined and the market research is designed in such a way as to get the relevant data in the form of numbers or statistics.
• Lot of attention is given to selecting the statistical sample and quality of the analysis tools used.
• Data is refined and analyzed using mathematical tools to predict behavior, arrive at patterns or suggest financial models etc.

Uses of Quantitative Analysis

You can use Quantitative Analysis for a number of purposes like:

• Measure customer satisfaction and commitment
• Understand customer behavior and preferences
• Find your target audience and design marketing strategy accordingly
• Segmentation analysis and understanding dynamics of a market
• It gives enormous information on customer needs thereby helping businesses to improve their products and services.
• It’s used in a variety of fields like Scientific, Medical, Political, Social and Market research activities.

By designing effective quantitative research techniques, collecting data from an appropriate sample and conducting a thorough analysis, you can achieve accurate results in your organizational goals. Whether you are a businessman, a student or professional, quantitative analysis equips you to make better and informed decisions by using logical mathematical or statistical models.

Financial Analysis

Financial Analysis plays an integral role in business growth and shapes the future of an organization. Based on mathematical tools and models, Financial Analysis helps you in corporate governance, understanding the impact of financial statements and evaluates company performance. Financial Analysis can be defined as the process of understanding businesses, budgets and financial statements to predict and evaluate a company’s growth. This course gives a good insight into Financial ratios and their interpretation.

Financial Analysis involves the study of income statements, profit and loss statements, balance sheets, cash flow statements and various financial ratios to determine the profitability of a company. If you aspire to work in the field of banking, investment management, risk assessment and management or as a financial analyst, then you must thoroughly understand the concepts of financial analysis and tools. You can learn the fundamental mathematics behind Financial Analysis in this course.

Business owners and managers use different approaches to analyze the financial performance of their organization and take appropriate decisions. We shall touch upon some of the main tools used:

• Financial Ratios – These ratios are used to calculate economic indicators that compare the organization’s performance with a competitor or with industry standards. They help determine liquidity, asset turnover, profitability, financial leverage etc. to predict the company’s short-term and long-term performance. Examples are Price to Cash-Flow ratio, Price to Sales ratio, Retention Ratio, Debt to Capitalization ratio etc.
• Financial Statements – Company’s financial statements like Balance Sheet, P&L statements, Cash flow statements etc. are analyzed horizontally (year to year comparison) or vertically (using common size or percentage comparison) to arrive at business decisions.

You can learn more about Financial Reporting and Analysis in this CFA level course.

Whether it is Quantitative Research & Analysis or Financial Analysis for Business, their analytical models are based on mathematical sequences and series formulas. As we discussed earlier, Sequences and Series play an important role in various aspects of our lives. They help us predict, evaluate and monitor the outcome of a situation or event and help us a lot in decision making. Adopt these effective analytical tools and processes to make better technological products, invent life-saving drugs and medical instruments, make social impact or increase business profitability. You will be amazed to discover the power of number sequences and series in your day to day life!