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Summary

  • A set of numbers arranged in a definite order according to some rules is called a sequence or progression.
  • The expression of the sum of a sequence is called a series.
  • A sequence is called an arithmetic progression if the difference between any term and its preceding term is a constant.
  • The nth term of an A.P. is given by
     
    Tn a + (n – 1)d
  • The sum of ‘n’ terms in an arithmetic progression is given by
     
  • Between two given numbers, it is possible to insert any number of terms such that the series thus formed shall be an A.P. The terms inserted are called the arithmetic means.
  • To insert n arithmetic means between two given numbers ‘a’ and ‘b’ we take the common difference as  
  • The sum of n arithmetic means between a and b is given by  
  • A sequence of terms is said to be a geometric progression, if the ratio of any term to its preceding term is a constant.
  • The nth term of a G.P. is given by
     
    Tn ar n – 1
  • The sum of n terms of a G.P. is given by
  • For given two positive numbers
  • Between two given numbers, we can insert any number of terms such that the series thus formed shall be in G.P. The terms inserted are called the geometric means.
  • To insert ‘n’ geometric means between two numbers a and b, we take the common ratio as
     
     
  • The product of n geometric means between the terms a and b is




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