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If the numbers n-2, 4n-1 and 5n+2 are in AP, find the value of n?

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An important question from ML Agarwal of Class10 We have asked If the numbers n-2, 4n-1 and 5n+2 are in AP, find the value of n?
Class 10 ML Agarwal Arithmetic Progression chapter 9 question no 21

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  1. n2,4n1,5n+2 are in A.P.

    First term, a1=n2
    Second term, a2=4n1
    Third term, a3=5n+2

    Common difference (difference of two consecutive terms),
    d=a2a1=a3a2
    4n1(n2)=5n+2(4n1)
    4n1n+2=5n+24n+1
    3n+1=n+3
    2n=2

    n=1

    So,
    a1=n2=12=1
    a2=4n1=41=3
    and d=a2a1=3(1)=4

    nth term of an AP is ,
    an=a+(n1)d
    where,
    a=first term
    d=common difference

    Therefore,
    a4=a+3d=1+12=11
    a5=a+4d=1+16=15

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