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Deepak Bora
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Which term of this A.P. is zero. If the 3rd and the 9th terms of an A.P. are 4 and − 8.

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The question is given from NCERT Book of class 10th Chapter no. 5 Ex. 5.2 Q. 9. In the following question you have to find which term will be zero if 3rd term is 4 & 9th term is -8. Give the solution.

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  1. Solution:

     

    3rd term, a3 = 4

    9th term, a9 = −8

    We know ,

    an = a+(n−1)d

    Hence,

    a3 = a+(3−1)d

    4 = a+2d                                     ……………………… (i)

    a9 = a+(9−1)d

    −8 = a+8d                                  ……………………… (ii)

    By subtracting (i) from (ii),

    −12 = 6d

    d = −2

    From eq. (i),

    4 = a + 2(−2)

    4 = a − 4

    a = 8

    Let the nth term term of the A.P. be zero.

    aa + (n−1)d

    0 = 8 + (n−1)(−2)

    0 = 8 − 2n+2

    2= 10

    n = 5

    The 5th term of this A.P. is 0.

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