First Term and Common Difference of an AP


 
 
Concept Explanation
 

First Term and Common Difference of an AP

Arithmetic Progression (AP) is a sequence of numbers in order in which the difference of any two consecutive numbers is a constant value.

The first term of an A.P. is denoted by small a_{1} and common difference is denoted by d.

  • In the A.P. 3,5,7,9,...
  • First Term . small a_{1}=3

    Difference a_2-a_1=5-3=2

    Difference a_3-a_2=7-5=2

    As the difference in both the cases is same so the common difference small d=2

    For example,

    The series of natural numbers: 1, 2, 3, 4, 5, 6,… is an AP, which has a common difference between two successive terms (say 1 and 2) equal to 1 (2 -1).

     

    Sample Questions
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    Question : 1

    If the first term of an AP is -103 and 6th term is -153. Find its common difference.

    Right Option : C
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    Explanation
    Question : 2

    If the first term of an AP is 5 and 4th term is 20. Find its common difference.

    Right Option : A
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    Explanation
    Question : 3

    If an AP is given by : 23, 21, 19, 17. Find its commond difference

    Right Option : B
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    Explanation
     
     


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