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The first & the last term of an A.P are 17 & 350 respectively. If the C.d is 9 how many terms are there & what is their sum?

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The first & the last term of an A.P are 17 & 350 respectively. If the C.d is 9 how many terms are there & what is their sum?

ML Aggarwal (avichal publication)  Arithmetic Progression chapter 9, question no.5

Please a give a detailed of this question as it is very important for board examination

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  1. Let a and d are first term and common difference for an AP.

    Number of terms of AP is n

    Last term =nth term =l=an

    We have a=17,d=9,l=350

    We know a+(n1)d=350

    17+(n1)9=350

    (n1)9=35017

    (n1)9=333

    n1=333/9

    n1=37

    n=37+1

    n=38

    Therefore, number of terms in given AP  is n=38

    Sum of n terms of AP is Sn

    Sn=2n(a+l)

    here n=38

    S38=238[17+350]

           =19×367

    S38=6973

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