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Two APs have the same common difference. The difference between their 100th term is 100, what is the difference between their 1000th terms? Q.12

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What is the best solution for exercise 5.2 of math in arithmetic progressions of class 10th. It is very important type of question. How i solve easily this question Two APs have the same common difference. The difference between their 100th term is 100, what is the difference between their 1000th terms?

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  1. Let, the first term of two APs be a1 and a2 respectively

    And the common difference of these APs be d.

    For the first A.P.,we know,

    an = a+(n−1)d

    Therefore,

    a100 = a1+(100−1)d

    a1 + 99d

    a1000 = a1+(1000−1)d

    a1000 = a1+999d

    For second A.P., we know,

    an = a+(n−1)d

    Therefore,

    a100 = a2+(100−1)d

    a2+99d

    a1000 = a2+(1000−1)d

    a2+999d

    Given that, difference between 100th term of the two APs = 100

    Therefore, (a1+99d) − (a2+99d) = 100

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

    Difference between 1000th terms of the two APs

    (a1+999d) − (a2+999d) = a1a2

    From equation (i),

    This difference, a1a= 100

    Hence, the difference between 1000th terms of the two A.P. will be 100.

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