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Deepak Bora
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Find the 31st term of an A.P. Whose 11th term is 38 and the 16th term is 73.

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The question is given from NCERT Book of class 10th Ch. no. 5 Ex. 5.2 Q. 7. In the following question you have to find the 31st term of an A.P whose 11th term is 38 & 16th term is 73. Give the answer briefly.

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1 Answer

  1. Given that,

    11th term, a11 = 38

    and 16th term, a16 = 73

    We know that,

    an = a+(n−1)d

    a11 = a+(11−1)d

    38 = a+10d ………………………………. (i)

    In the same way,

    a16 = a +(16−1)d

    73 = a+15d ………………………………………… (ii)

    On subtracting equation (i) from (ii), we get

    35 = 5d

    d = 7

    From equation (i), we can write,

    38 = a+10×(7)

    38 − 70 = a

    a = −32

    a31 = a +(31−1) d

    = − 32 + 30 (7)

    = − 32 + 210

    = 178

    Hence, 31st term is 178.

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