Sequences and Series

Arithmetic progressions are the sequences in which the terms continue to increase or decrease with a steady value. The difference that is observed in those terms is called the common difference for that progression. Common differences can be used to find the factors of a progression that are not in sight just yet. Using this […]

In mathematics, a sequence is a list of elements (most of the time, numbers) in which the order of the elements is important. The parts of this composition are organised in a certain way. In real life, we come across sequences in a variety of settings. The numbers of houses in a row, the amount

Mathematics is all about sequences and series. A sequence is a list of elements that allows for any number of repetitions, whereas a series is the sum of all elements. For instance, 2, 4, 6, 8, 10 is a five-element sequence, and the corresponding series is 2+4+6+8+10, with the sum of the series being 30.

Carl Fredrich Gauss, a German mathematician and physicist, discovered in 1796 that every positive integer may be expressed as the sum of three triangular numbers. The depiction of numbers in the form of an equilateral triangle arranged in a series or sequence is known as the triangular number sequence. The numerals are arranged in the

The method of differences is a trick method to solve those sequence and series problems that do not come in the categories of traditional progression series. We can easily solve an AP and a GP series by applying the respective formulas for the summation to find the value of the nth term of the series,

In an arithmetic progression, ‘a’ is used for the first term of that A.P. By adding to it the value of common difference, it is possible to find out the further terms of that progression. It means that by using the first term of a progression we can come to know about a lot of

When we explore the things we see in everyday life, it is not hard to spot a pattern or sequence. One puzzle that scientists puzzled over for many years was the sequence of sunflower petals. Research has found that these petals are part of Arithmetic Progression. Previously, people would need a calculator to sum the

Introduction The concept of finding the sum of first n numbers is highly used while studying arithmetic progression (or AP). To realize the concept behind finding the sum of first n natural numbers, students need to be familiar with arithmetic progression, the sum of n terms, and how it is derived from these concepts. These

Odd numbers are those that cannot be evenly divided by two. It is impossible to split it equally into two independent integers. When we divide an odd integer by two, we get a residue. Odd numbers include 1, 3, 5, 7, and so on. Even numbers are the polar opposite of odd numbers.  Sum of

The arithmetic progression series is the one that progresses with a constant value. The value at which an A.P series progresses is known as the series’ common difference (d). The arithmetic progression formulas do the calculation of the A.P series; these formulas are used to determine values such as the nth term of the series