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Rajan@2021
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If sum of the 3rd and 8th term of an ap is 7 and the sum of the 7th and 14th term is -3.find the 10th term

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An important question from ML Agarwal (avichal publication) If sum of the 3rd and 8th term of an ap is 7 and the sum of the 7th and 14th term is -3.find the 10th term.
ML Publication, Class 10, Arithmetic Progression Chapter 9, question no. 16

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  1. nth term tn​=a+(n−1)d

    a= First term
    d= Common difference
    n= number of terms
    tn​=nth term

    a3​+a8​=7a+2d+a+7d

    =72a+9d=7⟶(i)

    a7​+a14

    =−3a+6d+a+13d

    =−32a+19d=−3⟶(ii)

    From (i) & (ii)
    2a+9d=72a+19d=−3

    −10d=10d=−1,a=8.

    a10​=a+9d=8+9(−1)=−1

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