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Rajan@2021
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Find the sum of first n terms of an AP whose nth term is (5-6n). Hence, find the sum of its first 20 terms.

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One of the most important question from arithmetic progression chapter in which we are to find the sum of first 20 terms whose nth term is (5-6n).

Book – RS Aggarwal, Class 10, chapter 5C,  question no 3

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  1. Given: an=56n
    Find some of the terms of AP:
    Put n=1, we get a1=1= first term
    Put n=2, we get a2=7= second term
    Common difference=d=a2a1=7(1)=6

    Sum of first n terms:
    Sn=n/2[2a+(n1)d]
    =n/2[2+(n1)(6)]
    =n(23n)

    Sum of first 20 terms:
    S20=20/2[2(1)+(201)(6)]
    =10[2114]
    =1160
    Sum of its first 20 terms of AP is 1160.

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