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Deepak Bora
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The sum of three numbers in AP is 3 and their product is -35. Find the numbers.

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An Important question based on Arithmetic progression Chapter of R.S Aggarwal book for ICSE & CBSE Board.
Here you have to find the numbers of AP with the help of their given sum and their product.
This is the Question Number 4 Exercise 11 B of RS Aggarwal Solution.

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  1. Let a – d, a, a + d are three numbers in AP.
    their sum = a – d + a + a + d = 3
    3a = 3
    or a = 1
    Again,
    Their Product = (a – d) x a x (a + d) = -35
    a(a² – d²) = -35
    (1² – d²) = -35
    or d = ±6
    d = 6 or d = -6
    We have 2 conditions here:
    At a = 1, d = 6
    Numbers are: -5, 1 and 7
    At a = 1 and d = -6
    Numbers are : 7, 1, -5

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