## Progressions and Series

Theory

Progressions and Series is one of the three important topics in the quantitative section in CAT and a significant number of questions appear in the examination from this section every year. Some of the questions from this section can be very tough and time consuming while the others can be very easy. The trick to ace this section is to quickly figure out whether a question is solvable or not and not waste time on very difficult questions. Some of the questions in this section can be answered by ruling out wrong choices among the options available. This method will both save time and improve accuracy. There are many shortcuts which will be of vital importance in answering this section. We will try and upload a few to help students.

Formula
• Arithmetic Mean = $$\frac{x_{1}+x_{2}+x_{3}…x_{n}}{n}$$
• Geometric Mean = $$\sqrt[n]{x_{1}*x_{2}*x_{3}…x_{n}}$$
• Harmonic Mean = $$\frac{n}{\frac{1}{x_{1}}+\frac{1}{x_{2}}+\frac{1}{x_{3}}+...+\frac{1}{x_{n}}}$$
Theory
• Arithmetic Mean $$\geq$$ Geometric mean $$\geq$$ Harmonic Mean
• The equality holds true if and only if all the terms are equal.
Formula

Sum of the first n terms:

• Arithmetic Progression $$(2a+(n-1)d)*\frac{n}{2}$$
• Sum of the first n natural numbers is $$\frac{n(n+1)}{2}$$
• Sum of the squares of the first n natural numbers is $$\frac{n(n+1)(2n+1)}{6}$$
Formula
• Sum of the first 'n' terms of a Geometric Progression is $$\frac{a(r^{n}-1)}{r-1}$$
• Sum of an infinite geometric progression is $$\frac{a}{1-r}$$