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Rajan@2021
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Find the sum of the following arithmetic series. 5+(−41)+9+(−39)+13+(−37)+17+…..+(−5)+81+(−3).

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A basic and conceptual question from arithmetic progression chapter in which we have to find sum of given arithmetic series

5+(41)+9+(39)+13+(37)+17+.....+(5)+81+(3).

RS Aggarwal, Class 10, chapter 5C, question no 2(iv).

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  1. 5+(41)+9+(39)+13+(37)+17+....+(5)+81+(3)
    The given series is combination of two AP’s.
    Let A1=5+9+13+.....+77+81
    and A2=413937......(3)

    For A1:
    First term =a=5
    Common difference=d=2
    Last term =l=81
    Now, using formula:
    81=5+(n1)4
    n=20
    Thus, there are 20 terms in AP.
    Now,
    Find the sum of these 76 terms:
    S20=n/2[a+l]
    =20/2(5+81)
    =860
    Sum of 20 terms of this AP is 860.

    For A2:
    First term =a=41
    Common difference =d=2
    Last term=l=3
    Now, using formula:
    3=41+(n1)2
    n=20
    Thus, there are 20 terms in AP.
    Now,
    Find Sum of these 76 terms:
    S20=n/2[a+l]
    =20/2(413)
    =440
    Sum of 20 terms of this AP is 440.

    Therefore, Sum of total terms: 860440=420.

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