Sequence and Series – Patterns and Progressions in Mathematics

Sequence and Series is an important topic in mathematics that deals with ordered lists of numbers and the sum of their terms. A sequence is an arrangement of numbers written in a specific order according to a fixed rule or pattern. Each number in a sequence is called a term. When the terms of a sequence are added together, the result is called a series. This topic helps students recognize numerical patterns and apply logical reasoning to solve problems efficiently.

One of the most common types of sequences is the Arithmetic Progression (AP), in which the difference between consecutive terms is constant. For example, 2, 5, 8, 11, … is an arithmetic sequence with a common difference of 3. Another important type is the Geometric Progression (GP), where each term is obtained by multiplying the previous term by a fixed non-zero number called the common ratio. For instance, 3, 6, 12, 24, … is a geometric sequence with a common ratio of 2.

Apart from AP and GP, students also study special sequences such as harmonic progression, Fibonacci sequence, and recursive sequences. Each of these has unique properties and applications. Formulas related to the nth term and the sum of n terms are used to solve a wide range of numerical and real-life problems.

Sequence and series have wide applications in physics, economics, computer science, and engineering. They are used to model population growth, calculate compound interest, analyze algorithms, and study motion and waves. In daily life, many situations such as installment payments, savings plans, and patterns in nature can be understood using sequences and series.

In competitive examinations like NDA, CDS, and other defence and engineering entrance tests, questions from sequence and series test a candidate’s analytical ability, speed, and accuracy. A strong command over this topic not only helps in scoring well in mathematics but also develops pattern recognition and problem-solving skills, which are essential for higher studies and practical applications.

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