Sequences and Series

  • Introduction to Sequences

    The word sequence denotes certain objects or events occurring in same order. In itself, a sequence is a set of numbers arranged in some specific manner. Applications of sequences can be found in many areas including in the process of analyzing Economic data and certain areas of physics. Also, sequence are of importance in developing […]

  • Arithmetic Sequence or Arithmetic Progression

    An arithmetic sequence or Progression (abbreviated as A.P) is a sequence in which each term after the first is obtained by adding to the preceding term, a fixed number which is called the common difference. In other words, quantities are said to be in Arithmetic Sequence, when they increase or decrease by a by common […]

  • Arithmetic Series

    The sum of an indicated numbers of terms in a sequence is called a Series. The series obtained by adding the terms of an arithmetic progression is called Arithmetic Series. For example, the sum of the first seven terms of the sequence is the series, The above series is also named as the partial sum […]

  • Application of Arithmetic Sequence and Series

    Example: Tickets for a certain show were printed bearing numbers from to . Odd number tickets were sold by receiving cents equal to thrice of the number on the ticket while even number tickets were issued by receiving cents equal to twice of the number on the ticket. How much amount was received by the […]

  • Geometric Sequence or Geometric Progression

    Introduction: Geometric sequence is a second type of sequence. One important application of geometric progression is in computing interest on saving account. Other applications can be found in biology and physics. Geometric sequence has also an application for finding the national income or population for any particular future year provided the values for the current […]

  • Geometric Series

    The series obtained by adding the terms of a G.P. is called the geometric series. Let be the sum of the first terms of the G.P. The term is , the term is , etc. Hence                           --- (1) Multiplying both members of (1) by , we get                         --- (2) On subtracting each side […]

  • Infinite Geometric Series

    A geometric sequence in which the number of terms increases without bound is called an infinite geometric series.             If the absolute value of the common ratio is less than , , the sum of terms, always approaches a definite limit as increases without bound. As we have proved that the sum of a finite […]

  • Application of Geometric Sequence and Series

    In this tutorial we discuss about the related problems of application of geometric sequence and geometric series. Example:                                                        A line is divided into six parts forming a geometric sequence. If the shortest length is cm and the longest is cm, find the length of the whole line. Solution:                         Given that                         , , […]