Deepak Bora
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If two A.P have the same common difference. The difference b/w their 100th term is 100. What is the difference between their 1000th term.

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The question is given from NCERT Book of class 10th Chapter no. 5 Ex. 5.2 Q. 12. In the following question you have to find the difference between the 1000th term as said in the above question. Give the solution of the above question.



1 Answer

  1. Solution:

    Let, the 1st term of two AP’s be a1 and a2 ;

    The c.d of the AP’s be ” d ” .

    For 1st A.P

    an = a+(n−1)d


    a100 = a1+(100−1)d

    a1 + 99d

    a1000 = a1+(1000−1)d

    a1000 = a1+999d

    For 2nd A.P ,

    an = a+(n−1)d


    a100 = a2 + (100−1)d

    a2 + 99d

    a1000 = a2 + (1000−1)d

    a2 + 999d

    It is given that the difference between 100th term of the two APs = 100

    i,e (a1 + 99d) − (a2 + 99d) = 100

    a1a2 = 100         ………………………….. (i)

    Diff. b/w 1000th terms of the two APs

    (a1+999d) − (a2+999d) = a1a2

    From eq. (i),

    This diff.  , a1a= 100

    The difference between 1000th terms of the 2 A.P’s will be 100.

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