Mathematical Algorithms - Sequence & Series Last Updated : 22 May, 2024 Summarize Comments Improve Suggest changes Share Like Article Like Report Mathematical algorithms are step-by-step procedures used to solve math problems. This article looks at sequences and series, which are important parts of these algorithms. Sequences are ordered sets of numbers, while series are the sums of these numbers. Understanding sequences and series is vital for solving complex math problems, modeling real-world situations, and developing advanced computer techniques. This article will give you a clear overview of the key ideas, uses, with some practice problems of mathematical algorithms involving sequences and series.. What is Sequence? A sequence is an arrangement of a set of numbers in a particular order defined by some rule. If a 1 , a 2 , a 3 . . . is a sequence then 1, 2, 3 denotes the position of the elements in the sequence. A sequence can be finite or infinite. Some well-known sequences are: Arithmetic Sequence Geometric Seqeunce Harmonic Sequence Fibonacci Sequence Juggler Sequence Padovan Sequence Aliquot Sequence Moser-de Bruijn Sequence Stern-Brocot Sequence Newman-Conway Sequence Sylvester’s sequence Recaman’s sequence What is a Series? A series is formed by adding the elements of the sequence. If a 1 , a 2 , a 3 . . . is a sequence then the series is given as a 1 + a 2 + a 3 + . . . Note that the series refers to the indicated sum of the sequence, not the sum itself. Difference between Sequence and Series: Sl. No. Sequence Series 1 It is a set of elements that follow a particular pattern. A Series is the sum of the elements of a sequence. 2 Order of the element is very important. Order of the elements is not so important. 3 Finite Sequence: 1, 2, 3, 4, 5 Infinite Sequence: 1, 2, 3, . . . Finite Series: 1 + 2 + 3 + 4 + 5 Infinite Series: 1 + 2 + 3 + . . . Easy Problems on Sequence and Series: Tetrahedral Numbers Rectangular (or Pronic) Numbers Program to check if N is a Pentagonal Number Hexagonal Number Octagonal number Nonagonal number Decagonal Numbers Program to print Arithmetic Progression series Program for N-th term of Arithmetic Progression series Program to print GP (Geometric Progression) Program for N-th term of Geometric Progression series Program to find sum of first n natural numbers Sum of first n even numbers Lucas Numbers Tribonacci Numbers Keith Number Disarium Number Pell Number Hailstone Numbers Program for Perrin numbers Medium Problems on Sequence and Series: Program for sum of arithmetic series Find N Arithmetic Means between A and B Program for sum of geometric series Find N Geometric Means between A and B Program for harmonic mean of numbers Harmonic progression Sum Sum of squares of first n natural numbers Sum of square of first n odd numbers Sum of square of first n even numbers Nicomachu’s Theorem Sum of cubes of first n odd natural numbers Sum of cubes of first n even numbers Squared triangular number (Sum of cubes) Square pyramidal number (Sum of Squares) Centered hexagonal number Program for centered nonagonal number Carol Number Woodall Number Taxicab Numbers Ludic Numbers Sum of the series 5+55+555+.. up to n terms Hard Problems on Sequence and Series: Program for sum of cos(x) series Program to print binomial expansion series Find m-th summation of first n natural numbers Sum of series 2/3 – 4/5 + 6/7 – 8/9 + ——- upto n terms Sum of the series 0.6, 0.06, 0.006, 0.0006, …to n terms Sum of the series 1, 3, 6, 10… (Triangular Numbers) Sum of the Series 1 + x/1 + x^2/2 + x^3/3 + .. + x^n/n Sum of the Series 1/(1*2) + 1/(2*3) + 1/(3*4) + 1/(4*5) + . . . . . Sum of the series 1 + (1+2) + (1+2+3) + (1+2+3+4) + …… + (1+2+3+4+…+n) Sum of series M/1 + (M+P)/2 + (M+2*P)/4 + (M+3*P)/8……up to infinite Sum of the series 1.2.3 + 2.3.4 + … + n(n+1)(n+2) Sum of Series (n^2-1^2) + 2(n^2-2^2) +….n(n^2-n^2) Program to find the sum of a Series 1 + 1/2^2 + 1/3^3 + …..+ 1/n^n Program to get the Sum of series: 1 – x^2/2! + x^4/4! -…. upto nth term Efficient Program to Compute Sum of Series 1/1! + 1/2! + 1/3! + 1/4! + .. + 1/n! Program to find Sum of a Series a^1/1! + a^2/2! + a^3/3! + a^4/4! +…….+ a^n/n! Find n-th term of series 1, 3, 6, 10, 15, 21… Finding nth term of any Polynomial Sequence Quick Links: Recent Articles on Series! Practice problems on Mathematical Algorithms Comment More infoAdvertise with us Next Article Mathematical Algorithms - Sequence & Series H harendrakumar123 Follow Improve Article Tags : Mathematical School Learning DSA Sequence and Series Practice Tags : Mathematical Similar Reads DSA Tutorial - Learn Data Structures and Algorithms DSA (Data Structures and Algorithms) is the study of organizing data efficiently using data structures like arrays, stacks, and trees, paired with step-by-step procedures (or algorithms) to solve problems effectively. Data structures manage how data is stored and accessed, while algorithms focus on 7 min read Quick Sort QuickSort is a sorting algorithm based on the Divide and Conquer that picks an element as a pivot and partitions the given array around the picked pivot by placing the pivot in its correct position in the sorted array. 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