Mathematical Algorithms | Sequence & Series What is Sequence? A sequence is an arrangement of a set of numbers in a particular order defined by some rule. If a1, a2, a3 . . . 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 a1, a2, a3 . . . is a sequence then the series is given as a1 + a2 + a3 + . . . 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, 5Infinite Sequence: 1, 2, 3, . . . Finite Series: 1 + 2 + 3 + 4 + 5Infinite Series: 1 + 2 + 3 + . . . Some practice problems on Sequence and Series: Easy: 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 Intermediate: 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: 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 Last Updated : 26 Sep, 2023 Share your thoughts in the comments Add Your Comment Please Login to comment...