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Prove that no matter what the …

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Prove that no matter what the real numbers and b are,the sequence with nth term a+nb is always an A.P. What is the common difference?

    • Posted by Anubhab Majumder 6 years, 9 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Dharmendra Kumar 6 years, 9 months ago

    Let an =a+nb where a and b are real numbers.

    Then put n=1we get a1=a+b

    Put n=2  a2=a+2b

    Put n=3  a3=a+3b

    Put n=4  a4=a+4b......and so on

    Now a2-a1= a+2b-(a+b)=a+2b-a-b=b

    a3-a2=a+3b-(a+2b)=a+3b-a-2b=b

    a4-a3=a+4b-(a+3b)=a+4b-a-3b=b ........

    So we get  a2-a1=a3-a2=a4-a3=..........=b

    Clearly the difference between two consecutive terms are same.

    Hence the given sequence of real numbers is in an A.P. with common difference d=a2-a1=a3-a2=a4-a3=..........=b

     

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