Question

What is sequence and series?

Answer 1

Hint: We first explain the concept of sequence and series. We name different types of sequence and series like A.P. and G.P. We then take an example and its components to understand the concept better.

Complete step by step answer:
Now let us start by defining the terms sequence and series. A sequence can be defined as a list of items or objects which have been arranged in a sequential way. A series can be defined as the sum of all the terms in a sequence. However, we must note that there has to be a definite relationship between all the terms of the sequence.
There are many types of series where we have arithmetic progression, geometric progression, harmonic progression. We also have infinite series where the series is not bounded.
For example, for geometric progression we express the geometric sequence in its general form.
We express the terms as ${{t}_{n}}$, the ${{n}^{th}}$ term of the series.
The first term be ${{t}_{1}}$ and the common ratio be $r$ where $r=\dfrac{{{t}_{2}}}{{{t}_{1}}}=\dfrac{{{t}_{3}}}{{{t}_{2}}}=\dfrac{{{t}_{4}}}{{{t}_{3}}}$.
The formula being ${{t}_{n}}={{t}_{1}}{{r}^{n-1}}$.
One such sequence will be $3,6,12,24,48......$ and the series of the same sequence will be
$3+6+12+24+48+......$.

Note:
The sequence can be both increasing or decreasing sequence where the common difference or ratio is a negative number or in the domain of $\left| r \right|<1$. We need to solve problems based on formulas to understand the fundamentals which are similar to forming the sequence occurring in repeated formation.